Vedanta C. Math - 4 Re-print Final (2078)

Unit Perimeter, Area and Volume

11

11.1 Perimeter - The distance all the round
Classwork - Exercise

1. Each room of the graphs represents 1 cm length. Let's tell and write
how far Popeye has to walk to get round each rectangle.

cm cm cm

cm cm cm


2. Let's add all sides of these plane figures. Then, tell and write the

perimeter of each figure.

a) b) 6 cm

3 cm 3 cm 2 cm 2 cm

6 cm
4 cm
Perimeter of rectangle
Perimeter of triangle

= + + = =+++=

In this way, the distance all the way round is the perimeter of a plane figure.

So, perimeter of a triangle = total of lengths of its 3 sides

Perimeter of a rectangle and square = total of lengths of its 4 sides

199Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

11.2 Perimeter of rectangle and square D l C
Lengths of a rectangle are equal. b
B
So, AB = CD = l (length) b
Breadths of a rectangle are also equal.

So, BC = DA = b (breadth) A l

Perimeter of the rectangle = total lengths of its 4 sides

= AB + BC + CD + DA

= l + b + l + b = 2l + 2b = 2(l + b)
Lengths and breadth of a square are equal.
Sl R It means all 4 sides of a square are equal.
So, PQ = QR = RS = SP = l
ll

P l Q Perimeter of the square = total lengths of its 4 sides

= PQ + QR + RS + SP

= l + l + l + l = 4l

Exercise - 11.1

Section A - Classwork

1. Let's tell and write the perimeters of these plane figures as quickly as

possible. 4 cm 2 cm

a) b) c)
2 cm
4 cm 3 cm

3 cm
3 cm
2 cm

5 cm 4 cm 2 cm

Perimeter = cm Perimeter = cm Perimeter = cm

2. Let's tell and write the perimeters of these plane shapes as quickly as
possible.

a) Sides of a triangle are 2 cm, 3 cm and 4 cm, perimeter =

b) Sides of a triangle are 5 cm, 4 cm and 6 cm, perimeter =

c) l = 3 cm and b = 2 cm, perimeter of the rectangle =

d) l = 5 cm and b = 3 cm, perimeter of the rectangle =

e) l = 2 cm, perimeter of the square =
f) l = 3 cm, perimeter of the square =

vedanta Excel in Mathematics - Book 4 200 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Perimeter, Area and Volume

3. Perimeter of a rectangle = 2 (l + b). Let's put the value of l and b, then
find the perimeter of rectangle.

a) l = 3 cm, b = 2 cm then 2(l + b) = =

b) l = 4 cm, b = 3 cm, then 2(l + b) = =

c) l = 5 cm, b = 2 cm, then 2(l + b) = =

4. Perimeter of a square = 4 × l. Let's put the value of l, then find the
perimeter of squares.

a) l = 3 cm, then 4 × l = =

b) l = 4 cm, then 4 × l = =

c) l = 5 cm, then 4 × l = =

Section B

5. Let's find the perimeter of the following plane shapes.

a) b) R c) F 2 cm E
3 cm
C
4 cm S D 2 cm C

6 cm 5 cm 4 cm
2 cm
2 cm

A 3 cm B P 4 cm Q A B

4 cm

6. Let's identify whether these figures are rectangle or square. Then, find
their perimeters using the formula 2(l + b) or 4 × l.

a) 3 cm b) 2.5 cm c) 4 cm

3 cm

3 cm
2.5 cm
2.5 cm

2 cm

2 cm

3 cm 2.5 cm

4 cm

7. a) Let's find the perimeter of triangles whose three sides are:

(i) 4 cm, 5cm, 7 cm (ii) 3.5 cm, 6.5 cm, 8 cm

201Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

b) Let's find the perimeter of rectangles using formula.

(i) l = 5 cm, b = 4 cm (ii) l = 6.5 cm, b = 5.5 cm

c) Let's find the perimeter of squares using formula.

(i) l = 6 cm (ii) l = 7.5 cm

Let's read these problems carefully, then solve them.

8. a) The rectangular surface of a book is 24 cm long and 24 cm
18 cm breadth. Find the perimeter of the surface.

18 cm

b) The length of a rectangular garden is 60 m and its breadth is 40 m.
Find the perimeter of the garden.
c)
A rectangular ground is 150 m long and 110 m wide.

(i) Find the perimeter of the ground.
9. a)
(ii) If you run around the ground, how many metres do you cover in
one round?

The length of a square surface of a paper is 12 cm. Find the perimeter
of the surface.

b) A square swimming pool is 75 m long.

(i) Find the perimeter of the pool.

(ii) If you swim round the edges of the pool, how many metres do you
swim in one round?

10. It's your time - Project work!

a) Let's measure the length and breadth of your maths book using a
30 cm - scale. Then, find the perimeter of its surface.

b) Let's measure the length and breadth of your exercise book using a
30 cm - scale. Then, calculate the perimeter of its surface.

c) Let's measure the length and breadth of the surface of your desk
(or table) using a measuring tape. Then, find its perimeter.

d) Let's measure the length and breadth of the surface of white (or black)
board in your classroom. Then, find its perimeter.

vedanta Excel in Mathematics - Book 4 202 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Perimeter, Area and Volume

11.3 Area - Space covered by a surface
Classwork - Exercise

1. Let's observe the surface of these pairs of objects. Write 'G' for the
greater and 'S' for the smaller surface.

a) b) c)


d) e) f)



2. Let's tell and write any two pairs of objects inside your classroom: one
has greater and another has smaller surface.

a) A has the greater surface than a

b) A has the smaller surface than a

Do you know a greater surface covers greater space and it has more area? A
smaller surface covers smaller space and it has less area.

11.4 Area of rectangle and square 1 cm
In the given square, the length of its each side is 1 cm.
1 cm 1 cm
The surface of the square covers the space 1 cm length by
1 cm breadth. 1 cm

So, the area of this square is 1 square centimetre. We write it as 1 sq. cm.

203Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

Classwork - Exercise

1. The area of each square is 1 sq. cm. Let's tell and write the area of these

rectangles.

a) b) c)



Area = Area = Area =

2. Each square room represents the area of 1 sq. cm. Let's research and
investigate the formula (rule) to find the area of rectangle.

a) Area of this rectangle = 12 sq. cm.

Number of rooms along length = 4 and along breadth = 3

length × breadth = 4 × 3 = 12 sq.

So, area of rectangle = length × breadth = l × b

b) Area of this rectangle =

Number of rooms along length = and along breadth =

length × breadth = × =

So, area of rectangle = =

c) Area of this rectangle =

Number of rooms along length = and along breadth =

length × breadth = × =

So, area of rectangle = =

In this way, area of a rectangle = length × breadth = l × b

In the case of a square, its length and breadth are equal.

So, area of a square = length × breadth = length × length= l × l

vedanta Excel in Mathematics - Book 4 204 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Perimeter, Area and Volume

Exercise - 11.2

Section A - Classwork

1. The area of each square room of the graph is 1 sq. cm. The area of each
1
half of the square room (triangle) is 2 sq. cm. Let's tell and write the
area of these plane shapes.



2. Let's tell and write the area of these rectangles or squares as quickly
as possible.
a) b) c)

b = 4 cm
b = 2 cm

b = 3 cm

l = 5 cm l = 2 cm l = 3 cm
Area =
Area = Area =

Section B

3. Let's find the area of rectangles by using formula.

a) l = 5 cm , b = 2 cm b) l = 4 cm, b = 3 cm c) l = 7 cm, b = 4 cm
d) l = 6 cm, b = 5 cm e) l = 8 cm, b = 6 cm f) l = 10 cm, b = 7 cm

4. Let's find the area of squares by using formula.

a) l = 3 cm b) l = 4 cm c) l = 5 cm

d) l = 7 cm e) l = 9 cm f) l = 10 cm

205Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

Let's read these problems carefully, then solve them.

5. a) The rectangular surface of a mobile phone is 9 cm 6 cm
long and 6 cm wide. Find the area of its surface.
9 cm

b) Length of the rectangular surface of a 8 cm
geometry box is 16 cm and its breadth is
8 cm. Find the area of its surface. 16 cm

c) The rectangular floor of a room is 10 m long and 8 m broad. Find the
area of the floor in sq. m.

6. a) The given greeting card is in the shape of a square. 12 cm
Its length is 12 cm. Find the area of the surface of 12 cm
the card.

b) The length of a square pond is 90 m. Find the area of the pond.

c) The given photo frame is in the shape of a square
and it's length is 21 cm. Find the area of the surface
of the frame.

It's your time - Project work!

a) Let's measure the length and breadth of the given objects using a 30 cm
-ruler. Then, find the area of the surface of the objects.

Objects Length (l) Breadth (b) Area

Math book

Exercise book

vedanta Excel in Mathematics - Book 4 206 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Perimeter, Area and Volume

b) Let's measure the length and breadth of the surface of the given objects using
a measuring tape. Then, calculate the area of the surface.

Objects Length (l) Breadth (b) Area

Desk

Table
White/black board

Classrooom

11.5 Volume - space occupied by an object

Let's take a full glass of water. Immerse
a stone into the water. Now, let's discuss
the answers of the following questions.

a) What happened when the stone is
immersed into the water?

b) Does the water overflow?
c) What caused the overflow of water?
d) Why did the water overflow?
A stone is a solid object. When it is immersed into water, it occupies same

space in the water. The space is provided by the overflowing water.
The space occupied by a solid object is the volume of the solid object.

11.6 Volume of cube

The given solid is a cube. The length, breadth, and height of a cube are equal.

In the given cube, its length, breadth and height are 1 cm

each.

So, it occupies 1 cube centimetre (cu. cm.) space. 1 cm
Its volume is 1 cubic centimetre (cu. cm.). 1 cm 1 cm
1 cu. cm = 1 cm × 1 cm 1 × cm

= length × breadth × height

207Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

So, the volume of cube = length × breadth × height

= length × length × length

=l×l×l

Cubic centimetre (cu. m.) and cubic metre (cu. m.) are the units of volume.

1 cubic metre (cu. m.) = 1 m × 1 m × 1 m

11.7 Volume of cuboid

The given solid is a cuboid. It is made up of joining 3 cubes. Each cube has
volume of 1 cu. cm. So, the volume of this cuboid is 3 cu. cm.

3 cu. cm = 3 cm × 1 cm × 1 cm 1 cm
= length × breadth × height

=l×b×h 1 cm 1 cm 1 cm 1 cm

Volume of cuboid = l × b × h

Volume of this cuboid = 16 cu. cm

2 cm = 4 cm × 2 cm × 2 cm

4 c m 2c m = length × breadth × height
=l×b×h

Exercise - 11.3

Section A - Classwork

1. Let's tell and write which one can occupy more space. Then, write
which one has more volume.

A occupies more space.
A juice box A match box So, has more volume.

A occupies more space.

A laptop A mobile So has more volume.

vedanta Excel in Mathematics - Book 4 208 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Perimeter, Area and Volume

A occupies more space.

So, has more volume.

A geometry box A book

2. Let's tell and write the answer as quickly as possible.

a) A cube occupies the space of 8 cu. cm. What is the volume of the
cube?

b) A cubical box occupies the space of 27 cu. cm. What is the volume of the
box?

c) A book occupies the space of 180 cu. cm. What is the volume of the
book?

d) The volume of a cube is 64 cu. cm. How much spaces does it
occupy?

e) The volume of a brick is 720 cu. cm. How much space does it
occupy?

3. Each cube represents a volume of 1 cu. cm. Let's count the number of
cubes. Then tell and write the volume of each solid.

a) b) c)

Volume = Volume = Volume =
d) e) f)

Volume = Volume = Volume =
g) h) i)

Volume = Volume = Volume =

Section B
4. Let's find the volume of cubes by using formula.

a) l = 2 cm b) l = 3 cm c) l = 4 cm d) l = 5 cm

e) l = 6 cm f) l = 7 cm g) l = 10 cm h) l = 12 cm

209Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

5. Let's calculate the volume of cuboids by using formula.
a) l = 4 cm, b = 3 cm, h = 2 cm b) l = 5 cm, b = 4 cm, h = 1 cm
c) l = 6 cm, b = 4 cm, h = 3 cm d) l = 9 cm, b = 5 cm, h = 4 cm
e) l = 10 cm, b = 7 cm, h = 5 cm f) l = 15 cm, b = 10 cm, h = 8 cm
6. Let's calculate the volume of the following solid objects.

a) b) c)

1cm

2cm
4cm

15cm
10cm
2cm 20cm
2cm
2 cm 2cm 10cm 10cm

d) e) f)

2cm 3cm 9cm

15 cm 8 cm 5cm

7. a) A cubical die is 3 m long. Find its volume. How much space does it

occupy?

b) A sweet is in the shape of a cube and its length is 2 cm. Find its volume.
How much space does it occupy?

c) A cubical box is 8 cm long. Find its volume. How much space does it
occupy?

8. a) A chocolate bar is 6 cm long, 3 cm wide, and 2 cm thick. Calculate its
volume.

b) A geometry box is 16 cm long, 8 cm wide, and 3 cm high. Find its volume.

c) A book is 24 cm long, 18 cm broad ,and 2 cm thick. Find its volume.

It's your time - Project work!

9. a) Let's measure the length, breadth and thickness of your maths book
using a 30 cm - ruler. Then, find its volume.

b) Let's measure the length and height of your geometry box. Then, find
its volume.

vedanta Excel in Mathematics - Book 4 ?

210 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Unit Geometry

12

12.1 Point, line, and line segment - Looking back
Classwork - Exercise

1. Let's choose the correct answer from the box and fill in the blanks.

straight line point line segment curved line

a) The dot P represents a P B
b) AB is a A Y
c) XY is a X Q
d) PQ is a P

2. Let's tell and write ' vertical', 'horizontal', or 'slanting' in the blank spaces.

a) AB is a line segment. C BA

b) AC is a line segment.

c) BC is a line segment. AB C

3. Let's name the vertical, horizontal, and slanting line segments.

a) is a vertical line segment. P R Q
b) is a horizontal segment. Q R P
c) is a slanting line segment.

12.2 Measuring the length of line segments

We use a centimetre - scale (or ruler) to measure the length of a line segment.
We also use it to draw the given length of a line segment.

1 cm 4.5 cm 8.4 cm 11.7 cm

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

10 mm =

211Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

In a centimetre - scale, 1 cm is divided into 10 equal parts. Each part
represents 1 millimetre (mm).

So, 1 mm = 1 of 1 cm = 0.1 cm and 5 mm = 5 of 1 cm = 0.5 cm and so on.
10 10

Exercise - 12.1

Section A - Classwork

1. Let's tell and write the name of straight line, line segment, curved line,

vertical line, horizontal line, and slanting line in the blanks.

XD

A BP Q MN AB

Y C

a) is a straight line. b) is a straight line segment.

c) is a curved line. d) is a vertical line segment.
e) is a horizontal line segment.

f) is a slanting line segment.

2. Let's tell and write the correct answer as quickly as possible.

a) How many millimetres (mm) make 1 cm?

b) Express 5 mm in cm.

c) A straight line segment is 3 cm 4 mm. Express this length in the decimal
of centimetres.

d) A straight line segment is 5.6 cm. The length of the line segment is

cm mm.

3. Let's measure and write the length of line segments.

a) A B b)P Q

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 80 80.5 19 19.5 120 120.5.513131.15.514241.25.515351.35.516461.45.5175 7.5 8 8.5 9 9

AB = 3.5 cm PQ = N
c) X Y d)M

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.05.5 91.5.5 102..55 131..55 142..55 153..55 164..55 7.5 8.5

0 1 2 3 4 5 6 7 80 91 102 131 142 153 164 157 8 9

XY = MN =
212 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

Geometry

4. Let's measure and write the length of sides of these triangles.

a) A b) R

AB = PQ =

BC = QR =

CA = RP =

BC PQ

5. Let's measure and write the length of sides of these rectangle and square.

a) D C b) H G

AB = EF =
BC =
CD = FG =

DA = GH =

AB HE =

EF

Section B

6. Let's draw straight line segments of the given lengths.

a) 3 cm b) 4 cm c) 7 cm d) 3.5 cm

e) 4.4 cm f) 6.5 cm g) 5.8 cm h) 8.2 cm

7. a) Let's draw a vertical line segment of the length 5 cm.
b) Let's draw a horizontal line segment of the length 4.5 cm.

c) Let's draw a slanting line segment of the length 7.3 cm.

It's your time - Project work!

8. a) Let's draw a vertical line segment. Measure and write its length.
b) Let's draw a horizontal line segment. Measure and write its length.

c) Let's draw a slanting line segment. Measure and write its length.

9. a) Draw a triangle ABC. Measure and write the length of its sides. Then,
calculate the perimeter of the triangle.

b) Draw triangle PQR. Measure and write the length of its sides. Then, find
the perimeter of the triangle.

213Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

12.3 Angle - Looking back

Classwork - Exercise

1. Let's look around your classroom and tell a few number of corners that
you observed.

C In the given figure, name of the angle is ∠ABC or ∠CBA.

B The point B at which an angle is made is called the vertex

of ∠ABC. The straight line segments AB and BC that make
A ∠ABC are called the arms of ∠ABC.

Let's tell and write the correct answer as quickly as possible. B

2. a) Straight line segments AO and BO meet each other at
the point

b) Name of the angle made by AO and BO at the point A
O is O

c) The vertex of ∠AOB is

d) The arms of ∠AOB are and .

R Q Z
PY X
3. a) Name of two angles in the given
figures are
and

b) Between ∠PQR and ∠XYZ, the
greater angle is

12.4 Measurement of angles outside inside
scale scale
The given figure is a protractor. Can
you identify a protractor inside your
instrument box? We use protractor to
measure angles. It is also used to draw
angles of the given measurement.

Degree is the unit of measurement of
angles. Degree is represented by the symbol (°). So, we write 30 degree as
30°, 45 degree as 45°, and so on.

vedanta Excel in Mathematics - Book 4 214 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Geometry

Now, study the following illustrations carefully and learn how to measure
the given angles.

BQ

AO OP

In this case, we use outside scale. In this case, we use inside scale.
So, ∠AOB = 60°. So, ∠POQ = 110°.

12.5 Construction of angles C

Let's learn to construct angles by
using a protractor.

Construct ∠ABC = 50°.

(i) Draw an arm AB and place your BA
protector on it as shown in figure.

(ii) Count round the edge from 0° to 50°, and mark C.

(iii) Remove the protractor and join BC, using a ruler and a sharpen pencil.

Now, you have constructed ∠ABC = 50°.

Exercise - 12.2

Section A - Classwork

1. Let's tell and write the names, vertices and arms of the following angles:

a) A b) F c) P

O BE D OR

Name Name Name
Vertex
Vertex Vertex Arms

Arms Arms vedanta Excel in Mathematics - Book 4

215Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Geometry

2. Let's compare the size of each pair of angles using the signs '<' or '>'.

a) R C b) Y XE

Q PB A OF G



3. Let's tell and write the names and measurements of these angles.

a) b)

R

C

A B QP

∠ ABC = =
d)
F
c) Z

E DX Y

= f) =
e)
B D

O A OC

= =
216 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

Geometry

4. Let's measure the sizes of these angles using protractor. Tell and write
the measurements as quickly as possible.

a) b) N c) X

A

B CO MO Y
∠ ABC =
e) D = =
d) R
f) R

Q P S T
F
E
=
= =

Section B

5. Answer the following questions.
a) What is an angle?
b) What do you mean by vertex and arms of an angle?
c) In ∠PQR, name its vertex and arms.
d) What are the vertex and arms of ∠PRQ?
e) How do you write 70 degree by using the symbol of degree?
f) What is the instrument used to measure angles?

6. Let's construct the following angles by using protractor:

a) 30° b) 40° c) 50° d) 60° e) 70° f) 80°
l) 105°
g) 90° h) 100° i) 120° j) 45° k) 75°

7. It's your time!

a) Let's draw two straight line segments using a ruler and a sharpen pencil
such that the angle between them is less than 90°. Name the angle and
measure its size using protractor.

b) Let's draw two straight line segments using a ruler and a sharpen pencil
such that the angle between them is greater than 90°. Name the angle
and measure its size using a protractor.

217Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

12.6 Types of angles by their sizes
According to the sizes of angles, they are categorised into the following

different types:

CC
C

BA B A BA
∠ABC is less than 90°. ∠ABC is 90°. ∠ABC is greater than 90°.
It is an acute angle. It is an obtuse angle.
It is a right angle.

180° B A

B A
C

C BA C ∠ABC is 360°.
∠ABC is 180°. ∠ABC is greater than 180°. It is a complete turn angle.
It is a reflex angle.
It is a straight angle.

The table given below shows the types of angles at a glance.

Types of angles Size Examples
1. Acute angle
2. Right angle Between 0° and 90° 10°, 20°, 80°, 89°, ...
3. Obtuse angle
4. Straight angle Exactly 90° 90°
5. Reflex angle
6. Complete turn Between 90° and 180° 91°, 120°, 160°, 179°, ...

Exactly 180° 180°

Between 180° and 360° 181°, 195°, 270°, 300°, ...

Exactly 360° 360°

Exercise - 12.3
Section A - Classwork

1. Let's choose the correct answer from the box and fill in the blanks.

acute angle obtuse angle right angle
straight angle reflex angle complete turn angle

a) ∠ABC is 90°. ∠ABC is

b) ∠PQR is less than 90°. ∠PQR is

vedanta Excel in Mathematics - Book 4 218 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Geometry

c) ∠XYZ = 210°. ∠XYZ is

d) ∠EFG = 180°. ∠EFG is

e) ∠AOB is 360°. ∠AOB is

f) ∠DEF = 150°. ∠DEF is

2. Let's write the types of angle shown by each of the following angles:

a) b) c)


d) e) f)



3. Look at the angles marked below carefully. Estimate whether each of
them is acute, obtuse, right, or straight angle..

a) b) c)

d) e) f)

219Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

4. a) Which two angles below can be put together to make a right angle?

and


35° 55°
45° 60° 120°

b) Which two angles can make a straight angle? and

Section B

5. a) What are the different types of angles according to their sizes?
b) What are acute, obtuse, and reflex angles? Write any three examples of

each of these types of angles.

c) Write the measurement of each of the following types of angles.

(i) right angle (ii) straight angle (iii) complete turn angle

d) Write a pair of angles whose sum is a right angle.
e) Write a pair of angles whose sum is a straight angle.

6. Let's categorise the following angles as acute, right, obtuse, straight,
reflex, and complete turn angles.

20°, 95°, 75°, 135°, 90°, 250°, 180°, 300°, 360°

7. Let's observe our National Flag and answer the following questions.

a) Name an angle that has vertex P. N

b) How many acute angles are there in the flag? Name any PE
3 acute angles.

c) How many right angles are there in the flag?

d) What type of angle is ∠ANE? AL

8. a) If the sum of x° and 30° is a right angle, find I got it!
the value of x°. x° + 30° = 90°
or, x° = 90° – 30° = 60°
b) If the sum of y° and 50° is a right angle, find
the value of y°.

c) If the sum of p° and 100° is a straight angle, find the value of p°.
d) If the sum of x° and 150° is a straight angle, find the value of x°.

vedanta Excel in Mathematics - Book 4 220 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Geometry

9. It's your time - Project work!
a) Let's make a paper-clock. Rotate the hour-hand and

minute-hand. Then, find out what types of angles are
formed at:
(i) 2 o'clock (ii) 4 o'clock (iii) 6 o'clock (iv) 7 o'clock (v) 9 o'clock
b) Let's cut 5 pairs of paper strips of equal size. Stick each pair of strips
using glue and make acute, right, obtuse, straight and reflex angles.
12.7 Plane figures (or shapes)

Let's discuss about the answer of the following questions.
a) What is the shape of the surface of the traffic signal board?

b) What is the shape of the surface of the book?

c) What is the shape of the surface of the given cubical die?

d) What is the shape of the surface of the given coin?

Triangle, rectangle, square, circle, etc. are called the plane figures. The
shape of the surface of a triangle is triangular, a rectangle is rectangular, a
square is square shape, and a circle is circular.

12.8 Triangle

Let's take a sheet of paper and fold it along one of its corner
as shown in the figure. Now, cut the folded corner. The cut
out part represents a triangle. The shape of this part is

triangular.

It is a triangle ABC. We write triangle ABC as DABC.

C

We use the symbol 'D' for the word 'triangle'.

AB, BC, and CA are 3 sides of DABC.

A B ∠A, ∠B, and ∠C are 3 angles of DABC.

A, B, and C are 3 vertices of DABC.

221Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

12.9 Types of triangles by sides

Let's read the length of three sides of each of these triangles. Then, learn to
classify them into 3 types - Scalene, isosceles, and equilateral triangle.

C RZ

4cm 3cm 3cm 3cm 3cm
2cm

A 3cm B P 4cm Q X 3cm Y

All three sides are not Two sides PR and QR All three sides are
equal. So, DXYZ is an
equal. So, DABC is a are equal. So, DPQR is equilateral triangle.

scalene triangle. an isosceles triangle.

12.10 Types of triangles by angles

Let's read the size of angles of each of these triangles. Then, learn to

classify them into 3 types - acute-angled, obtuse-angled, and right-
angled triangles.

AP X

80° 30° 50°

60° 40° 110° 40° R 90° 40°
B C Q Y Z

All three angles are One of the angle One of the angles
acute. So, DABC is (∠PQR) is obtuse. So, (∠XYZ) is a right angle
an acute-angled DPQR is an obtuse- (90°). So, DXYZ is a
triangle. angled triangle. right-angled triangle.

Exercise - 12.4

Section A - Classwork

1. Let's tell and write the name, vertices, sides, and angles of these triangles.

a) R Name Vertices , ,

Sides , ,

Angles , ,

QP 222 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

Geometry

b) F Name Vertices , ,
Sides ,,
4cm 4cm
E D Angles , , 5cm
c)
2. Let's tell and write the types of triangles.

a) b) 4cm

3cm 4cm
4cm 4cm

5cm

triangle triangle triangle
e) f)
d)
30° 60° 40°
50° 30° 120° 80°

90° 40°

triangle triangle triangle

3. Let's tell and write the types of triangles. triangle.
a) Any two sides of a triangle are equal. It is

b) None of the sides of a triangle are equal. It is triangle.
triangle.
c) All three sides of a triangle are equal. It is

d) One of the three angles of a triangle is obtuse angle.

It is triangle.

e) One of the three angles of a triangle is a right angle.

It is triangle.

f) All three angles of a triangle are acute angle.

It is triangle.

Section B

4. a) What are the different types of triangles according to the length of their
sides?

b) What are the different types of triangles according to the size of their

angles?

223Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

c) What type of triangle is an isosceles triangle?

d) What type of triangle is an equilateral triangle?

e) What type of triangle is a right-angled triangle?

f) DABC is an equilateral triangle. If the side AB = 5 cm, write the length of
the sides BC and CA.

5. It's your time - Project work!
a) Let's name any three objects which have triangular shaped surface.

b) Draw a triangle using a ruler. Write the vertices of the triangle. Then,
write the name, sides, and angles of the triangle.

c) Let's open your instrument box and find two triangular shaped
instruments. What are these instruments called?

d) Let's use one of the two set-squares to draw an isosceles triangle. Name
the triangle and write its 3 sides. Measure the length of 3 sides. Which
are the two equal sides of the triangle?

e) Let's use another set-square to draw a right-angled triangle. Name the
triangle and measure the size of its 3 angles using a protractor. Which
one is the right angle?

12.11 Quadrilaterals D S R
A C Q
In the given figures, ABCD is a quadrilateral.
PQRS is also a quadrilateral. A quadrilateral BP
is a plane shape bounded by 4 straight line
segments. A rectangle and a square are the
special type of quadrilaterals.

Rectangle
Let's discuss about the answer of the following questions.
a) What is the shape of the surface of your maths book?
b) What is the shape of the surface of the walls of your classroom?
c) What is the shape of the surface of your desk (or table)?

vedanta Excel in Mathematics - Book 4 224 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Geometry

D lC ABCD is a rectangle.
90° 90° AB, BC, CD, and DA are the 4 sides of the rectangle.
∠A, ∠B, ∠C, and ∠D are the 4 angles of the rectangle.
b b AB and CD are the length (l) of the rectangle.
90°
90°
A lB

BC and DA are the breadth (b) of the rectangle.

(i) Lengths of a rectangle are always equal. So, AB = CD = l

(ii) Breadths of a rectangle are always equal. o, BC = DA = b.

(iii) Each angle of a rectangle are always equal and of 90° (right angle).

So, ∠A = ∠B = ∠C = ∠D = 90°

Square Sl R
PQRS is a square. 90° 90°

PQ, QR, RS, and SP are the 4 sides of the square. l l

∠P, ∠Q, ∠R, and ∠S are the 4 angles of the square. 90° 90°
(i) All four sides of a square are always equal.
Pl Q

So, PQ = QR = RS = SP = l

(ii) All four angles of a square are always equal and they are 90°.

So, ∠P = ∠Q = ∠R = ∠S = 90° (a right angle)

12.12 Circle

Let's take a coin and place it on a sheet of paper. Move the

tip of a sharpen pencil along it's edge. What type of shape

is formed? Can you tell the name of any two objects which

have circular shape?

The figure given alongside is a circle. It is a Diameter
rounded plane figure. Centre

A OB
Radius
O is called the centre of the circle.
AB is the diameter of the circle. C

OC is the radius of the circle. circumference

OA and OB are also the radii (plural of radius) of the circle.

The rounded boundary line is the circumference of the circle.

225Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

(i) Radii (plural of radius) of the same circle are always equal.

So, OC = OA = OB.

(ii) Length of a diameter of a circle is always two times the length of its
radius.

So, AB = 2 × OC or 2 × OA or 2 × OB

Similarly, OC = 1 AB, OA = 1 AB and OB = 1 AB
2 2 2

Exercise - 12.5

Section A - Classwork

1. Let's tell and write the name, vertices, sides, and angles of the given
rectangle and square.

G F Vertices , , ,

a) Name

Sides , , ,

E Angles , , ,

D

Z Y Vertices , , ,

b) Name

Sides , , ,

X Angles , , ,

W S

2. a) In the given rectangle PQRS, if PQ = 5 cm, R

QR = 4 cm, find the length of RS = 4 cm

and SP = P 5 cm Q
D C

b) In the given square ABCD, if AB = 3.5 cm, find the length

of BC = , CD = and DA = A 3.5 cm B

HG

c) In the given rectangle EFGH, ∠E = ,

∠F = , ∠G = and ∠H = E

F

vedanta Excel in Mathematics - Book 4 226 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Geometry

d) In the given square KLMN, ∠K = , ∠L = N M

,

∠M = and ∠N =

KL

3. Let's tell and write the name of center, radius, and diameter of these
circles.

A Z X centre is

centre is

O radius is P radii are ,

C diameter is Y diameter is

B

Section B

4. Let's find the length of the sides marked by letters. G
2 cm
a) D x C b) S y R c)

H

A 4 cm B P 3 cm Q pF

ABCD is a rectangle. PQRS is a square. E
PQRS is a rectangle.

d) Z e) N 2 cm M f) A
p
b
2.5 cm D
3 cm 5 cm q
Y
W a y 4.5 cm C
c B ABCD is a rectangle.

X KxL
KLMN is a rectangle.
WXYZ is a square.

5. Let's find the size of angles marked by letters.

a) D C b) S R c) H d cG

a

xy b a b
AB PQ E F

ABCD is a square. PQRS is a rectangle. EFGH is a rectangle.

227Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry

6. Let's find the diameter of each circle.

a) B b) P c)

A 1.5cm O O 2cm R Y O Z
2.5cm

C Q X
radius = 2 cm radius = 2.5 cm
radius = 1.5 cm

7. Let's find the radius of each circle.

a) A b) D c) P R

4cm 5cm O
O EO F 6 cm

C diameter = 5 cm Q
B diameter = 6 cm

diameter = 4 cm

It's your time - Project work

8. a) Let's name any two objects which have rectangular shaped surface.
b) Let's name any two objects which have square shaped surface.
c) Let's name any two objects which have circular surface.

9. a) Let's measure the lengths and breadths of your maths book by using a
30 cm - scale.

(i) Are the lengths equal? (ii) Are the breadths equal?

b) Let's measure the lengths and breadths of your bed by using a measuring
tape.

(i) Are the lengths equal? (ii) Are the breadth equal?

12.13 Solid figures (or shapes)

Cube, cuboid, cylinder, sphere, cone, pyramid, etc. are called solid figures.
Solid figures are also called 3 dimensional figures or 3 - D figures. Length,
breadth, and height are the 3 dimensions.

Cube Face 1
The given solid figure is a cube. It has got 52
Edge 4 36
6 square faces, 12 edges, and 8 corners Corner
(vertices).

The length (l), breadth (b), and height (h).

vedanta Excel in Mathematics - Book 4 228 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Geometry

Cuboid Face 5 1
46 2
The given solid figure is a cuboid. It has Edge 3
got 6 square rectangular faces, 12 edges, Corner
and 8 corners (vertices).

A cuboid also has (l), breadth (b), and
height (h).

Cylinder Circular face
Curved surface
The given solid figure is a cylinder. It has got
2 circular faces, 1 curved surface, and 2 circular
edges. It does not have any corner (vertex).

Cone Circular edge
The given solid figure is a cone. It has got 1 circular Circular surface
Circular edge
face, 1 curved surface, circular edge, and 1 corner Curved surface
(vertex). Corner
Curved surface
Sphere
The given solid figure is a sphere. It does not have

any face, edge, and corner. It has a curved surface.

Exercise - 12.6

Section A - Classwork

1. Let's tell and write the names of these solid figures. Also name an

object similar to each of these shapes.

a) b)
It is a It is a

c) d)
It is a It is a

229Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Geometry f)
It is a
e)

It is a


2. Which solid shapes are these objects similar to?

a) b) c)


d) e) f)



3. Let's tell and write the number of faces. Edges and corners of these
solid shapes?

a) faces, edges

and corners.

b) faces, edges, and
c) corners. curved surface
circular faces,
edges

d circular faces Does it have any
curved surface faces, edges, and
corners. corners?

4. Let's tell and write the name of solid figures in the blank spaces.

a) A has 1 circular face, 1 curved surface, 1 edge, and 1 corner.

b) A has 6 rectangular faces, 12 edges, and 8 corners.

c) A has 2 circular faces, 1 curved surface, and 2 edges.

d) A has 6 square faces, 12 edges, and 8 corners.

?

vedanta Excel in Mathematics - Book 4 230 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Unit Statistics

13

13.1 Bar graph - Looking back
Classwork - Exercise

1. Let's study this horizontal bar graph and answer the given questions.

Favourite fruits The bars represent the number of students
who like different fruits.
Apple a) How many students like apple?
b) How many students like orange?

c) Which one is the least favourite
Mango fruit?



Orange



Banana

0 1 2 3 4 5 6 7 8 9 10 11 d) How many students participated in the

Number of students

survey?
2. Let's read this vertical bar graph and answer the questions.

a) What do the bars represent? 13 Annual result of class 4

b) Let's write the number of students in the 12

given table who got different grades. 11
10

Grades 'A' Grade 'B' Grade 'C' Grade Number of students 9
8
No. of students 7

6

c) In which grade did the highest number of 5

students pass? 4
3

d) How many students appeared in the annual 2
exam of class 4?
1
'B' 'C'
O Grade Grade
'A'

Grade

Result

231Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Statistics

The given graph is called a bar graph. Flowers in School Garden
It's a way to show and compare data, or 15
information.
14
13

A bar graph has four main parts: a title, Number of flowers 12
labels, a scale, and bars. 11

1. In the given bar graph, the title is 10
'Flowers in School Garden'. 9
8

2. Below the graph is the label 'Types of 7
6
Flowers'. Just below the bars, the types 5
flowers are written as 'Rose', 'Lily', and 4
'Daffodil'. 3

3. The scale is the set of numbers along 2 Lily Daffodil
the left side of the graph. It shows the 1
number of items. O

Rose

4. Bars are the rectangular vertical or Types of Flowers

horizontal boxes drawn to represent the given information.

Exercise - 13.1

Section A - Classwork

1. Let's tell and write the correct answer Number of students Favourite Sports
of the following questions. 11

a) What is the title of the bar graph? 10
9
b) What is the label of the bar graph? 8
7
6
c) How many students like cricket? 5
4
d) How many students do not like 3
football? 2
1
e) How many less students like table O
tennis than cricket?
Football Cricket Table Tennis
Types of Sports

f) Which is the most popular sport among the students?

g) Which is the least popular sport among the students?

h) How many students participated in the survey?

vedanta Excel in Mathematics - Book 4 232 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Statistics

Section B

2. Let's draw bar graphs using the information given in the tables.

a) Careers Doctor Teacher Pilot b) Events Quiz Sports Dance Music

No. of 7 94 No. of 20 50 25 10
Students Participants

Career Choices School Day Events
55
Doctor Number of participants 50
Teacher 45
40
Pilot 35
30
O 1 2 3 4 5 6 7 8 9 10 25
Number of students 20
15
10

5
O Quiz Sports Dance Music

Events

3. a) Class 4 students conducted a survey about which cartoon characters
they like. The table given below shows their responses:

Cartoon Characters Mickey Mouse Bugs Bunny Scooby Doo Daffy Duck

No. of students 12 8 59

Draw a bar graph using this information.

b) The table given below shows the number of votes received by the
candidates of school prefect in a school

Candidates AB CD
No. of votes 30 80 50 100

Draw a bar graph using this information.

c) The scores obtained by different houses in a Maths Quiz Contest are
given below in the table. Draw a bar graph using the information.

Houses Green House Red House Yellow House Blue House
Scores 60 40 50 35

233Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Statistics

4. It's your time - Project work!

a) Let's make a group of 5 students. Conduct a survey and find the number
of students from class 1 to class 5 in your school. Write the numbers in
the table and show the information in a bar graph.

Classes 1 23 45
No. of Students

b) Working on your own, or with a partner, or in a group, investigate the
following for the pupils in your class. Collect the statistics in a table
and then illustrate them in bar graphs.

(i) Their favourite subjects (ii) Their favourite sports

(iii) Their favourite vegetables

(iv) How do they usually come to school, by walking, or by school bus or
by own vehicles?

13.2 Measurement of temperature
How do you feel in the winter mornings? Hot or cold?

How do you feel in the summer days? Hot or cold?

How do you feel when you touch the recently cooked rice?

How do you feel when you touch an ice cube?
Temperature shows the hotness or coldness of an object. We can find

how much hot or cold an object is by measuring it's temperature.

We use an instrument called Thermometer to measure the temperature.

Wemeasuretemperature 234 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
usually in two units. They
are Degree Celsius (°C)
and Degree Fahrenheit
(°F).

Do you know? Water
boils at 100°C or
212° F. Water freezes at
0° or 32°F.

vedanta Excel in Mathematics - Book 4

Statistics

Exercise - 13.2

Section A - Classwork

1. Let's tell and write the correct answer in the blank spaces.

a) The hotness in an object is called its

b) The instrument which is used to measure the temperature
is

c) and are the two units that

we usually use to measure temperature.

d) Water boils at °C or at °F.

e) Water freezes at °C or at °F.

2. Let's write temperature shown in the following thermometers.

a)

b)

c)

d)

3. Nowadays, we usually use digital thermometers to measure our body
temperature. Let's tell and write the temperature in °F shown in these
thermometers.

a) 97.5°F b) 98 °F c) 100.5°F



4. Here are the maximum temperatures from the different cities of Nepal
one day in July. Tell and write the answer of the questions.

Ilam: 23°C Kathmandu: 26°C Nepalganj: 39°C
Biratnagar: 36°C Pokhara: 30°C Jumla: 20°C
Birgunj: 37°C Jomsom: 15°C Dhangadhi: 38°C


235Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Statistics

a) Which was the warmest city?

b) Which was the coldest city?

c) What was the difference in temperature of these two cities?

d) Which cities had temperature less than 30°?

e) BetweenIlamandPokhara,whichonewashottercity?

f) From the climatic point of view, which city do you prefer to visit?

Section B
5. a) Name the instrument which is used to measure temperature.
b) What are the two units of temperature?
c) How many degree Fahrenheit (°F) are there in 0°C?
d) How many degree Celsius (°C) are there in 212°F?

6. The given digital thermometer is showing the 98.6°F
normal temperature of human body.

a) What is the normal temperature of human body?

b) What does fever cause in the body temperature of a person?

c) What is it said if the body temperature of a person exceeds 100°F?

7. a) The temperature of cold water is 25°C. When it is warmed it's
temperature rises to 52°C. By how many °C is the temperature risen?

b) In the morning time the temperature was recorded 17.5°C. In the
afternoon the temperature increased by 12.5°C. What was the
temperature in the afternoon?

8. The pupils of class 4 measured the temperatures of a day at different times
in degree celsius (°C).

At 8:00 a. m.

At 12:00 noon
At 3:00 p. m.

At 6:00 p. m. 236 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

vedanta Excel in Mathematics - Book 4

Statistics

Write the temperatures at different times in a table and show the information
in a bar graph.

9. It's your time - Project work!

a) Let's take a digital or a clinical thermometer and measure your and family
members' body temperature. Does everybody has normal temperature?

b) Let's measure the body temperature of every student of your class. Does
everybody has normal temperature?

c) Let's visit the available website and find today's minimum and maximum
temperatures of your district, city, or nearby city.

13.3 Ordered pairs

Let's read the name of homes of a few animals.

Bird - Nest We can write these animals and their homes in
Lion - Den pairs in the following ways. (Birds, Nest),
(Lion, Den), (Dog, Kennel), and (Horse, Stable)
Dog - Kennel

Horse - Stable


In these pairs, the first member is always an animal and the second
member is its home. So, the animals and their homes are in the fixed pairs
of order. Such pairs are called ordered pairs.

In the given graph, a horizontal line OX and a vertical line OY are intersecting
at O. From O, the numbers along horizontal and vertical lines are
1, 2, 3, ... respectively. If you run 3 units along horizontal and jump 4 units

along vertical line, you reach at an apple. Y

So, the ordered pair (3, 4) represents 10
9
the position of the apple. Similarly, the 8
ordered pair (7, 3) shows the position 7

of mango and (5, 8) shows the position 6

of orange. 5

Thus, the ordered pair of numbers 4 Jump
(3, 4) means, 3 units horizontally (Run),
then 4 units vertically (Jump). 3

2
1 Run

O 1 2 3 4 5 6 7 8 9 10 X

237Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Statistics

Exercise - 13.3

Section A - Classwork

1. Let's tell and write the ordered pairs of these countries and their
capitals.

a) Nepal - Kathmandu b) India - New Delhi

c) China - Beijing d) Japan - Tokyo

2. Let's tell and write the position of children in the ordered pairs of
(Row, column).

Sahayata → (R1, C2) R1 Pratik Sahayata Nirjal
Dakshesh → (R3, C1)

a) Pratik →

b) Nirjal → R2 Priyasha Sayad Anamol
c) Priyasha →

d) Sayad → R3 Dakshesh Sunayana Shreyasha
e) Anamol → C1 C2 C3
f) Sunayana →
g) Shreyasha →

3. Let's tell and write the ordered pairs of numbers to show the position of

the fruits. Y

a) Mango → 10

b) Orange → 9
8

c) Apple → 7
6

d) Guava → 5

4

3

2

1

O 1 2 3 4 5 6 7 8 9 10 X

vedanta Excel in Mathematics - Book 4 238 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Statistics

4. Let's tell and write the ordered pairs Y
of numbers of the given points. 10

9

8

a) P → b) Q → 7 R B
6 S
c) R → d) S → 5 A
4P
e) A → f) B → 3

2
1Q

O 1 2 3 4 5 6 7 8 9 10 X

Y

10

5. Let's mark the points in the given graph 9
to show the ordered pairs of numbers 8
of the points. 7
6

a) A → (2, 4) b) B → (4, 2) 5
4

3

c) M → (3, 5) d) N → (5, 3) 2

1

e) P → (8, 6) f) Q → (6, 8) O 1 2 3 4 5 6 7 8 9 10 X

Section B
6. Let's write any 5 ordered pairs for each of the following statements.

a) The first member is the parent animal and the second is its baby animal.
b) The first member is the European country and the second is its capital.
c) The first member is odd number and the second is just the double of the

odd number.

d) First member is the half of even number and the second is the even
number.

239Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Statistics

7. From the graphs given below, let's write the ordered pairs of numbers
to show the position of each vertex of the shapes.

a) b)

Y Y

10 10

9 9 E
8F D
8 R
7 7
6C C
6 GH

5 Q 5
4S
4

3 3
2A 2A
P 1 B

1B O 1 2 3 4 5 6 7 8 9 10 X
O 1 2 3 4 5 6 7 8 9 10 X

8. It's your time - Project work!

a) Let's arrange your 9 friends in 3 rows and 3 columns. Then write the
position of each friend in the ordered pairs of (Row, Column).

b) Let's write the position of your 10 friends in the ordered pairs of
(Row, Column) inside your classroom. What is the ordered pair of your
position?

?

vedanta Excel in Mathematics - Book 4 240 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Unit Set

14

14.1 Set - A collection of objects - Looking back

Classwork - Exercise
1. The figures given below is a collection of plane and solid shapes.

A collection of shapes

a) Let's wrote the names of the plane shapes
and make a separate collection.

b) What are the members of this collection?

, A set of plane shapes
,

c) Let's write the names of solid shapes and
make another separate collection.

d) What are the members of this collection?

, A set of solid shapes
,

14.2 Set - A well-defined collection

In the given collection of children, Angkita Angkita Manoj Kalpana
is taller than Kalpana but shorter than
Manoj. Once, she belongs to the collection
of 'tall children', but again she does not
belong to the collection of 'tall children'.
Thus, the collection of 'tall children' is not
well-defined and it is not called a set.

241Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Set

Similarly, the collection of long rivers of Nepal, the collection of favorite
fruits, etc. are not well-defined collections. Therefore, these collections

are not sets.

1 On the other hand, the collection of odd numbers
37 5 less than 10 definitely includes the members 1, 3, 5,
9 7 and 9. So, it is a well-defined collection and it is

called a set.

A set is a collection of well-defined objects.

Exercise - 14.1

Section A - Classwork

1. Let's tell and write the names of these sets. Also write the members of
the sets.

a) 2
48
6

A set of A set of

Members are , , Members are , ,
,,

2. Let's tell and write any 3 members of each of these two sets.

a) b)

A set of domestic animals. A set of prime numbers
less than 10.

3. Let's cross out the object which does not belong to the set and write

the name of the set.

a) b)

It is a set of It is a set of
242 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

Set

c) d)

2 3 1 5 b i a e
7 9 o u

It is a set of It is a set of

4. Let's tick (√) to the well-defined collection.

a) A collection of high mountains of Nepal.

b) A collection of mountains of Nepal higher than 7000 m.

c) A collection of fruits.

d) A collection of delicious fruits.

Section B

5. Let's copy the well-defined collections and write the name of the sets.
a) A collection of name of 5 pupils of class four.
b) A collection of name of 5 tall pupils of class four.
c) A collection of name of 4 favourite vegetables.
d) A collection of name of 4 vegetables.
e) A collection of name of 5 rivers of Nepal.
f) A collection of name of 5 long rivers of Nepal.

6. Let's write the following collections.
a) Any 3 collection of objects which are not well-defined.
b) Any 3 collection of objects which are well-defined.

14.3 Methods of writing sets

We can write the members of a set in many ways. We shall discuss here
about 3 ways of writing the members of a set.

Diagrammatic method

Monday Sunday Tuesday 5723

Wednesday Thursday

Friday Saturday

A set of seven days of the week. A set of prime numbers less than 10

243Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Sets

Descriptive method
In this method, we describe the type of members of a set in words. For

example,
A set of seven days of the week.
A set of prime numbers less than 10 and so on.

Listing method

In this method, we list the members of a set inside the curly bracket { }.
The members are separated by using commas (,). We may name the set by
using a capital letter.

For example,
A = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
B = {2, 3, 5, 7}

Exercise - 14.2

Section A - Classwork

1. Let's tell and write the correct answers in the blank spaces.

a) In method, we write the members of a set inside
a circular diagram.

b) In method, we describe the types of members of
a set in words.

c) In method, we list the members of a set inside
the curly brackets.

2. Let's list the members of these sets in curly brackets.

a) e iu b) 4 6
o
a 2 8

A= B=

3. Let's tell and list any three members of these sets inside curly brackets.

a) A set of wild animals. W=

b) A set of domestic animals. D =

c) A set of aquatic animals. A =

d) A set of composite numbers less than 9. N =

vedanta Excel in Mathematics - Book 4 244 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Sets

Section B

4. Let's list the members of these sets in the curly brackets. Also name
the sets.

a) e n a b) 1 2 3 January
pl 45 c)

June July

5. Let's express these sets in descriptive method.

a) b) 1 3 5 f u
79 c)

or

6. Let's write these sets in diagrammatic method.

a) A set of three planets closer to the Earth.

b) A set of prime numbers between 10 and 20.

c) A set of the first five multiples of 2,

d) A set of vowels in English alphabets.

7. Let's rewrite the following sets in listing method. Also name the sets.

a) A set of three planets far away from the earth.

b) A set of any three instruments inside a geometry box.

c) A set of whole numbers less than 5.

d) A set of all possible factors of 12.

e) A set of the letters of the word 'four'.

8. Let's rewrite the following sets in descriptive method.

a) {mercury, venus, mars} b) {whale, dolphin, prawn, shark}

c) {1, 2, 3, 4, 5} d) {3, 6, 9, 12, 15} e) {h, o, u, s, e}

9. It's your time - Project work!

a) Let's look around your classroom. Let's select any four objects as the
members of a set.

(i) Let's write the set with these members in diagrammatic method.

(ii) Let's write the set in listing method. Also name the set.

(iii) Let's write the set in descriptive method.

b) Look around your house. Let's select any four objects as the members of

a set. Write the set in three different methods.

?

245Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Answers

Answers

Section B 1. Number System
5. a) 54 = 5 × 10 + 4 × 1 Exercise – 1.1

b) 270 = 2 × 100 + 7 × 10

c) 1325 = 1 × 1000 + 3 × 100 + 2 × 10 + 5 × 1 d) 3017 = 3 × 1000 + 1 × 10 + 7 × 1

6. a) 63 = 6 × 10 + 3 × 1 b) 542 = 5 × 100 + 4 × 10 + 2 × 1

c) 4507 = 4 × 1000 + 5 × 100 + 7 × 1 d) 20304 = 2 × 10000 + 3 × 100 + 4 × 1

7. a) T O b) H T O c) Th H T O d) T-th Th H T O

8. a) 672 b) 4853 c) 51491
2 × 1 = 2 3 × 1 = 3 1 × 1 = 1

7 × 10 = 70 5 × 10 = 50 9 × 10 = 90
6 × 100 = 600 8 × 100 = 800 4 × 100 = 400
4 × 1000 = 4000 1 × 1000 = 1000

5 × 10000 =50000

9. a) 84 b) 725 c) 408 d) 2077 e) 5346 f) 36187

10. a) 45 b) 180 c) 900

11. a) Nine thousand seventy-five b) Fifteen thousand nine rupees 12. a) Rs 7011 b) 10086

13. a) one b) two c) three d) seven e) nine

Exercise – 1.2

Section B

3 . a) L1 T-2th T5h H6 T1 O0 On e lakh twenty-five thousand si x hun dred ten.
Twenty-seven lakh eighteen thousand three hundred
b) T-l L T- th Th H T O nine.

2 7 1 8 309 Four crore seventeen lakh thirty-six thousand
c) C T-l L T-th Th H T O eighty-two.

4 1 7 3 6 08 2

d) T-c C T-l L T-th Th H T O Fifteen crore forty-four lakh nine
1 5 4 4 0 9 1 5 0 thousand one hundred fifty.

4. a) H-th T-th Th H T O One hundred fifty-seven thousand
1 5 7 3 2 0 three hundred twenty.

b) M H-th T-th Th H TO Three million two hundred seventy-one thousand
1 0 68 sixty-eight
3 2 7
c)
T-m M H-th T-th Th H T O Twenty-one million forty-nine thousand three

2 1 0 4 9 3 5 5 hundred fifty-five

d) H-m T-m M H-th T-th Th H T O Four hundred sixty million thirty-two
4 6 0 0 3 2 1 8 0 thousand one hundred eighty

vedanta Excel in Mathematics - Book 4 246 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

5. a) 26,908 – Twenty-six thousand nine hundred eight

b) 1,25,043 – One lakh twenty-five thousand forty-three

125,043 – One hundred twenty-five thousand forty-three

c) 38,04100 – Thirty-eight lakh four thousand one hundred

3,804,100 –Three million eight hundred four thousand one hundred

d) 5,06,09,050 – Five crore six lakh nine thousand fifty

50,609,050 – Fifty million six hundred nine thousand fifty

e) 43,00,85,027 –Forty-three crore eighty-five thousand twenty-seven

430,085,027 – Four hundred thirty million eighty-five thousand twenty-seven.

6. a) Lakh (Hundred thousand), 200000, 2 b) Ten-lakh (Million), 4000000, 4

c) Crore (Ten-million), 10000000,1 d) Ten-crore (Hundred- million), 300000000,3

7. a) 1 million b) 2 million c) 3 million d) 4 million e) 5 million f) 9 million

8. a)10 million b) 20 million c) 30 million d) 50 million e) 80 million f) 100 million

9. a) 10 lakh b) 60 lakh c) 70 lakh 10. a) 1 crore b) 4 crore c) 7 crore

11. a) 347000, three hundred forty-seven thousand

b) Rs 2580500, two million five hundred eighty thousand five hundred rupees

c) 30260000, thirty million two hundred sixty thousand

12. a) 147181 sq. km, one lakh forty-seven thousand one hundred eighty-one sq. km

b) Rs 4750300, forty-seven lakh fifty thousand three hundred rupees

c) Rs 120580000, twelve crore five lakh eighty thousand rupees

13. a) 740, 407 b) 8652, 2568 c) 96310, 10369 d) 875420, 204578 14. Please perform the given
project work. Compare your outcomes with your friends.

Exercise – 1.3

Section B

3. a) 40 b) Rs 230 c) 260 km d) 4,610

4. a) 500 km b) 700 c) Rs 15,900 d) 19,900 litres

5. a) 220, 200 b) 570, 600 c) 1,660 , 1,700 d) 34,850 , 34,900

Exercise – 1.4

Section B

3. a) 19 b) 27 c) 39 d) 44 e) 49 f) 78
g) 99 h) 246 i) 429 j) 865 k) 994 l) 2290

4. a) XVIII b) XXIX c) XXXVIII d) XLV e) LXVII

f) LXXXIX g) XCVI h) CCXL i) CCCXCII j) CDLIV

k) DXCIX l) DCXLIII m) CMLXXV n) MDIV o) MMCCCXC

5. Please perform the given project work and discuss with your friends in the class.

3S.e cat)io..n. B 147, 149, ... 2. Whole Numbers
145, Exercise – 2.1
4. a) ... , 304, 306, 308, ...
b) ... ,267, 269, 271, 273, ... c) ... , 591, 593, ... , 597, ...
b) ... , 406, 408, 410, 412, ... c) …,798, 800, 802, 804, ...

5. Please perform the given activities. Discuss about your investigation in your class.
6. Please perform the given activities.

247Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Answers

3. Fundamental Operations
Exercise – 3.1

Section B b) 1,220 kg c) 1,051 students d) 4,345 people e) Rs 465
8. a) Rs 840 g) 986 girls h) 2,288 men i) Rs 285 j) Rs 535
f) 376 l

9. a) 175, 320 b) 229, 407 c) 387, 712 d) 881, 1580 e) 2880, 5005 f) 3687, 8250

10. a) 941 b) 485 c) 60,550 d) 10,700 e) 203 kg 11. a) Rs 925 b) Rs 850

12. a) (i) 634 (ii) 1,090 b) (i) 456 (ii) 1,090 c) (i) Rs 3,035 (ii) Rs 4,820

13. a) Rs 4,000 b) Rs 2,535 c) Rs 6,740 d) Rs 650 e) Rs 165 f) Rs 150 g) Rs 195

h) Rs 165 i) Rs 1,035 j) Rs 2050 14. and 15. Please perform the given activities
individually or in group. Discuss the outcomes of the activities in the class.

Exercise – 3.2

Section B

8. a)160 b) 1600 c) 2100 d) 21000 e) 24000

f) 1100 g) 22000 h) 6000 i) 4500 j) 4800

9. a) 192 b) 322 c) 765 d) 216 e) 900 f) 1998

g) 4048 h) 1740 i) 6075 j) 13056 k) 31360 l) 560500

10. a) Rs 1,250 b) Rs 1,620 c) Rs 5,700 11. a) 300 eggs b) 144 pencils

c) 240 balls d) Rs 4,800 e) Rs 1,95,000 12. a) 5,000 kg b) 7,000 kg c) 11,340 ml
d) 306 g protein e) 2,160 calories f) 1,50,000 l g) 240 km h) 448 km i) 1,320 km

13. a) 364 days b) 144 months c) 5,475 days 14. a) 400 students b)270 chairs
15. and 16. Please perform the given project works. Discuss about your outcomes in the class.

Exercise – 3.3

Section B

9. a) 4 b) 40 c) 400 d) 40 e) 2 f) 20 g) 200 h) 20

i) 3 j) 5 k) 4 l) 70 m) 80 n) 80 o) 90 p) 90

10. a) Q =11, R = 3 b)Q = 12, R = 2 c) Q = 16, R = 1 d) Q = 12, R = 0
e) Q = 12, R = 0 f) Q = 106, R = 1 g) Q = 108, R = 2 h) Q = 104, R = 0
i) Q = 106, R = 0 j) Q = 103, R = 0 k) Q = 214, R = 1 l) Q = 212, R = 2

m) Q = 213, R = 1 n) Q = 153, R = 2 o) Q = 142, R = 0

11. a) Q = 1150, R = 2 b) Q = 1192, R = 3 c) Q = 1132, R = 0 d) Q = 1122, R = 2
e) Q = 1092, R = 0 f) Q = 1022, R = 2 g) Q = 1003, R = 0 h) Q = 449, R = 1
i) Q = 588, R = 0 j) Q = 751, R = 0

12. a) Q = 12, R= 0 b) Q = 12, R = 5 c) Q = 10, R = 6 d) Q = 15, R = 0

e) Q = 17, R = 6 f) Q = 9, R = 8 g) Q = 8, R = 2 h) Q = 42, R = 0

i) Q = 62, R = 10 j) Q = 73, R = 5 13. a) Rs 85 b) 5 kg c) Rs 96 d) 8 l

14. a) 15 dozens b) 25 crates c) 24 boxes 15. a) 100 kg b) 1000 kg c) 500 ml

16. a) 11 players b) 14 teams 17. a) 30 students b) 15 columns

18. a) 52 weeks b) 25 years c) 12 years

19. and 20. Please perform the given project works. Discuss about your outcomes in the class.

Exercise – 3.4

Section B

4. a) 23 b) 25 c) 19 d) 22 e) 15 f) 21 g) 20 h) 1 i) 27 j) 5

5. a) 14 b) 3 c) 32 d) 3 e) 5 f) 40 g) 72 h) 4 i) 32 j) 39 k) 5 l) 8

vedanta Excel in Mathematics - Book 4 248 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur