plain surface

Ex 5 9:35 PM

Monday, July 6, 2020

Find the area of following triangle

find the area of triangle
sides of triangle are

semi- perimeter s= .

we have ,

area of triangle=

=

2) find the area of following quadrilateral

sides of are 5,12,13

semi- perimeter s=

=15

we have ,

area of triangle=

=
=30

Area of parallelogram=

=

3) b) IN the adjoining figure, ABCD is a trapezium if AB=60 cm CD=77 cm
AD=26 and BC=25 find the area of given trapezium ABCD
solution:
Draw
PQ=AB=60 opposite sides of rectangle

In using pytha
In using pythagorous theorem
AP2=BQ2

mensuration Page 1

Area of ABCD=

4a) the perimeter of a triangular field is 30 cm and its sides are in the ratio of 11:12:5 . Find the area
of the field.
Solution
Ratio of sides 13:12:5
so, let the sides be 13x,12x,5x
Perimeter of triangle =
30=

sides of triangle are 13,12,5

semi- perimeter s= .=15

we have ,

area of triangle=

=

5a) if the perimeter of an equilateral triangle is 12 cm find its area
solution,
perimeter of equilateral triangle= 3a

12=3a
a=4

area of equilateral triangle =

6a) the base of an isosceles triangle is 12 cm and its perimeter is 32 . Find its area.
Solution ,
perimeter of a triangle = a+b+c
32=a+a+12 { a=b being isosceles ]
a=10
sides of triangle are 10,10,12

a=10 b=12

Area of isosceles triangle =

=

=
=

7a) if the area of an isosceles triangle is 240 and each of its equal sides is 26 cm . Find the length
of third side
solution
sides of triangle are 2x ,26,26

semi- perimeter s= .

we have ,

mensuration Page 2

we have ,
area of triangle=

240 =

240=
240=

let

240=

squaring on both sides

57600=676y -

100( y- 576 )=0
Either
Or
From I
substituting the value of y we get

From ii
if y= 576

8a) the perimeter of a triangle is 84 cm and area is 336 of one of the side is 30 cm fin its
others sides.
Solution
one side is 30 other sides are
Perimeter = 84
a+b+30=84
a=54-b
sides of triangle are a,b,30

mensuration Page 3

sides of triangle are a,b,30
semi- perimeter s=
we have ,
area of triangle=

336 =
336=
336=
squaring on both sides

112896=
224=

9a) two adjacent sides of parallelogram are 3 cm and 4 cm and one diagonal is 5 cm . Find its area
same as 2a
10a) the perimeter of right angle triangle is 60 cm and its area is 120 cm2 find the length of its sides
Solution ,
perimeter of a right angel triangle =

area of right angle =

by pythagorus

0=3600-120h -480
120h=1320
h=26
Substituging value of h we get
P+b=60-26
p= 34-b

mensuration Page 4

p= 34-b
puttting value is pb=240 we get

11a) An umbrella is made by stitching 10 triangle pieces of cloth of two different colors as shown in
the figure , each piece measuring 20 cm 50 cm and 50 cm . How much cloth is required for the
umbrella ?
sides of triangle are 20 cm 50 cm and 50 cm
s=

area of triangle =

Area of the cloth for umbrella=

11b)
An umbrella is made by stitching 8 triangle pieces of cloth of two different colors as shown in the
figure , each piece measuring 30,113 and 113 . How much cloth is required for the umbrella ? Find
the total cost of clothes at the rate of Rs 2 per cm2
Solution :
sides of triangle are 30,113 and 113
s=

area of triangle =

Area of the cloth for umbrella=

find the area of cloth for the umbrella

total cost =
=

Area of triangle if sides are give

Area of triangle =

where

Area of equilateral triangle = where a is the side of triangle

area of isosceles triangle =

Area of triangle =
where a= equal side and b= base

mensuration Page 5

Perimeter of triangle =sum of all sides
perimeter of equilateral triangle =3a

page 73
Q 1a)
Given side of triangle are 13 , 21,20

we have

we have =
Area of triangle
=
3d) =
in triangle ABC
using Pythagoras

Again
in triangle ABD
using Pythagoras

Area of ABACD= Area of ABC + Ara of ADC

3a)
i)
using Pythagoras theorem

BC=20

mensuration Page 6