MENSURATION 2D

MENSURATION

2D

1. Find Area of a triangle whose sides are 36 cm, "a"
15 cm and 39 cm. "b"

(A) 180 cm2 (B) 270 cm2 (A) a 4b2 a2 square units
4

(C) 225 cm2 (D) 360 cm2 a
2
2. In a triangular field having sides 30 m, 72 m (B) 2a2 b2 square units
and 78 m., the length of the altitude to the
side measuring 72 m is: b 4a2 b2 square units
4
(C)

(A) 25 m (B) 28 m (D) b a2  2b2 square units
2
(C) 30 m (D) 35 m
7. The perimeter of an isosceles triangle is 544
3. If the perimeter of a right-angled triangle is
56 cm and area of the triangle is 84 sq. cm, cm and each of the equal sides is 5 times the
then the length of the hypotenuse is (in cm) 6
base. What is the area (in cm2) of the triangle?

(A) 25 (B) 168 5
6
(C) 7 (D) 24
(A) 38173 (B) 18372
4. The sides of a triangle are 14 cm and 20 cm
the angle included between then is 30°. Find (C) 31872 (D) 13872

area of triangle. 8. The perimeter of an isosceles triangle is 72 cm.
If one of the equal sides is 26 cm then find
° area of triangle.

(A) 140 cm2 (B) 120 cm2

(C) 70 cm2 (D) 115 cm2 (A) 220 cm2 (B) 225 cm2

5. In an isosceles triangle, the measure of each (C) 240 cm2 (D) 260 cm2
of equal sides is 10 cm and the angle between
them is 45°, the area of the triangle is
9. The altitude drawn to the base of an isosceles
triangle is 8 cm and its perimeter is 64cm. The
° area of the triangle is-

(A) 25 cm2 (B) 25 2 cm2 8
2 64

(A) 105cm2 (B) 115cm2

(C) 50 2 25 2 cm2 (D) 25 3 cm2
2
(C) 120cm2 (D) 240cm2

6. If for an isosceles triangle the length of each 10. Perimeter of right angle isosceles triangle is (4 2 +4)
equal side is 'a' units and that of the third side cm. What is the length of its Hypotenuse ?
1 is 'b' units, then its area will be

(4 2 +4) drawn from the opposite vertex to side whose
length is 14 cm.

13 14 15

(A) 2 2 cm (B) 4 2 cm

(C) 2( 2 +1)cm (D) 4cm 14

11. If perimeter of isosceles right angle triangle is (A) 8cm (B) 11cm
'2P'. What is the area of triangle?
(C) 12cm (D) 9cm
'2P' 16.
The altitude drawn to the base of an isosceles
triangle is 24 cm and its perimeter is 64 cm.
The area of triangle is-

(A) P2(3+2 2 )cm2 (B) P2(3–2 2 )cm2

(C) P2(3+ 2 )cm2 2p (A) 150 cm2 (B) 168 cm2
(D) 2  2

12. The ratio of three sides of a triangle is 5 : 5 : 8. (C) 175 cm2 (D) 188 cm2
If the area of triangle is 12 cm2, then what is
the length (in cm.) of the equal sides? 17. Euclid has a triangle in his mind, its longest side
has length 20 mt and another of its side has
length 10 mt and its area 80 mt2. What is the
length of third side?

(SSC Delhi Police Constable

Exam. 05.12.2017 (IIIrd Sitting) 20 10
80 2
(A) 5 (B) 8

(C) 6 (D) 2.5

13. The ratio of base of two triangles is x : y and (A) 260 mt (B) 250 mt
that of their areas is a : b. Then athe ratio of
their corresponding altitudes will be: (C) 240 mt (D) 270 mt

x:y 18. The height of an equilateral triangle is 18 cm.
Its area is
a:b

(A) a : b (B) ax : by
x y

(C) ay : bx (D) x :b (SSC CGL Tier-II (CBE)
a y Exam. 30.11.2016)

14. Given that the ratio of altitudes of two triangles (A) 38 3 square metre
is 4 : 5, ratio of their areas is 3 : 2. The ratio of
theircorresponding bases is (B) 108 3 square metre
(C) 108 square metre
4:5
(D) 96 3 square metre
3:2 If the numerical value of the perimeter of an
equilaterasl triangle is 3 times the area of
(SSC CGL Tier-II Exam. 19. it, then the length of each side of the triangle
25.10.2015, TF NO. 1099685) is
(A) 8 : 15
(C) 5 : 8 (B) 15 : 8 3
(D) 8 : 5

15. Length of sides of a triangle are 13 cm, 14 cm
and 15 cm. Find the length of perpendicular

2

(A) 2 units (B) 3 units (C) 28 π cm2 (D) 32 π cm2
(C) 4 units (D) 6 units 3 3

20. If the length of each side of an equllateral tri- 25. If the difference between areas of the circum-
angle is increased by 2 unit, the area is founded circle and the incircle of an equllateral triangle
is 44 cim2, then the area of the triangle is
to be increased by 3 + 3 square unit. The

length of each side of the triangle is

(3+ 3 )

(Take π  22 )
7
(A) 3 unit (B) 3 unit

(C) 3 3 unit (D) 1+3 3 unit (A) 28 cm2 (B) 7 3 cm2

21. From a point inside an equilateral triangle the (C) 14 3 cm2 (D) 21 cm2

length of perpendicular to three sides are P1, P2 26. IN an isosceles triangle, the length of each
and P3. What is the length of each side? oequal side is twice the length of the third side.
The ratio of areas of the isosceles triangle and
P1, P2 an equilatteral triangle with same perimeter
P3 is

(A) P1 + P2 + P3 (B) 3 (P1 + P2 + P3)
3 2

2 (D) P1 + P2 + P3 (A) 30 5 : 100 (B) 32 5 : 100
(C) 3 (P1 + P2 + P3) 2

22. From a point inside an equilateral triangle the (C) 36 5 : 100 (D) 42 5 : 100
length of perpendicular to three sides are 6 cm,
8 cm and 10 cm. What is the area of triangle? 27. Let x denote the product side of triangle. Let y
denote the product of its semi-perimeter,
68 10 inradius and circumradius then y/x = ?

x
y

(A) 144 3 cm2 (B) 176cm2 y/x-

(C) 192 3 cm2 (D) 192 2 cm2 (A) 1/4 (B) 1/3

23. The perimeter of an equilateral triangle is 24 3 . (C) 1/6 (D) CND
What is the radius of incircle and circumcircle 28.
to the triangle- Ratio between base/side/height/perimeter of
two equilateral triangle is 5:4. What is the ratio
24 3 between area of two triangles ?

(A) 8cm, 4cm (B) 4cm, 8cm 5:4

(C) 4 3 cm, 8 3 cm (D) 4 2 , 8 2 cm (A) 5:4 (B) 25:16
24. The area of an equllateral triangle inscribed in
(C) 16:25 (D) 4:5
a circle is 4 3 cm3. The area of the circle is 29.
Points P and Q lie on sides AB and AC of tri-
43 angle ABC respectively such that segment PQ
is parallel to side BC. If the ratio of areas of
triangle APQ : triangle ABC is 25 : 36, then the
ratio of AP : PB is

(A) 16π cm2 (B) 22 π cm2 ABC AB AC P, Q
3 3

3

PQ, BC APQ (A) 768mt2 (B) 534mt2
AP : PB (C) 696.8mt2 (D) 684mt2
ABC 25 : 36

(SSC CGL Tier-I CBE (Exam) 34. A square field of site 500 mt it has compound
wall along its perimeter. At one of its corner a
01.02.2017 (Second Sitting)
triangular area of field is to be cordoned off by

(A) 5 : 6 (B) 1 : 5 exacting a straight line fence. Compound wall
(C) 6 : 5 (D) 5 : 1 and fence form it border. If length of fence is
100 mt. What is the max. area that can be

30. D and E are points on sides AB and AC of ABC. cordoned off.

DE is parallel to BC. If AD : DB = 2 : 3, what is 500 2
the ratio of area of ADE and area of quadrilat-
eral BDEC?

ABC AB AC D, E
AD : DB = 2 : 3 ADE
BDEC 100
(A) 2500mt2
(SSC CHSL (10+2) Tier-I CBE (B) 10,000mt2

(Exam) 21.08.2017) (C) 5000mt2 (D) 3750mt2

(A) 4 : 21 (B) 4 : 25 35. Length of three medians of a triangle are 9cm,

(C) 4 : 29 (D) 4 : 9 12cm and 15cm. What is the area of triangle?

31. If the lengths of the sides AB, BC and CA of a 9 12
triangle ABC are 10 cm. 8 cm and 6 cm re-
15

spectively and if M is the mid-point of BC and (A) 60cm2 (B) 54cm2
MN||AB to cut AC at N, then the area of the
trapezium ABMN is equal to
(C) 72cm2 (D) 96cm2

MN, BC AB, BC, CA 36. Length of sides of triangle are 10 cm, 21 cm
M BC and 17 cm. Find length of perpendicular drawn
ABMN from opposite vertese to side whose length is
10 cm.

(A) 18 sq. cm. (B) 20 sq. cm. 10 cm, 21 cm, 17 cm

(C) 12 sq. cm. (D) 16 sq. cm.

32. Through each vertex of a triangle, a line paral- (A) 8 cm (B) 14.2 cm
lel to the opposite side is drawn. The ratio of
the perimeter of the new triangle, thus formed, (C) 16.8 cm (D) 14.8 cm

with that of the original triangle is. 37. Given an etqruiainlagtleeraTl2triisanfogrlme Ted1 with side 24cm,
a second by joining mid

pbyoinjotionfinsigdemTi1d, then a tohfirTd2.trIiaf ntghliesTp3 rios cfoersms eodf
point

triangle continued, the sum of the areas in Sq

(A) 3 : 2 (B) 4 : 1 cm, of infinitely many such triangles T1, T2, T3,
..... will be–

(C) 2 : 1 (D) 2 : 3 T1
T3
33. Two sides of a plot measure 32 mt and 24 mt T2 T2
and the angle between them is a perfect right
angle. The other two sides measure 25 mt each

and other three angles are not right angle. What

is the area of plot? (A) 164 3 (B) 188 3

(C) 248 3 (D) 192 3

4

38. One side of an equilateral triangle is 36 cm. 41. In the adjoining figure a square of maximum
The mid points of its sides are joined to form possible area is circum scribed by the light
another triangle. Whose mid points are in turn angle triangle. ABC in such a way that one of
joint to form still another triangle. This pro- its side just dies on the hypotenuse of the tri-
cess continue in finitely. Find the sum of pe- angle. What is the area of the square
rimeters of all the triangles.

ABC

(A) 208 cm (B) 216 cm C
A
(C) 144 cm (D) 180 cm
B
39. ABC is a triangle in which angle A is right angle
AB = a, AC = b, CB = c what isthe length of
square APQR.

ABC A AB = a, AC =
b, CB = c APQR

abc (B) a2  b2  c2
(A) a 2  b2  ab abc

abc (D) None of these
(C) a 2  b 2  c 2

42. In the figure given below, XYZ is right angled

(A) a b c (B) a b triangle is which y=45° and x=90°ABCD is a
2 2 square isscribed in it whose area is 64 cm2.
What is the area of triangle XYZ?
a b ab
(C) a b (D) a b XYZ

40. In a right angle triangle ABC,AB=12 AC=15.A y=45° x=45° ABCD 64 cm2
square is inscribed in the triangle. One of the XYZ
vertices of square coincides with the vertex of
triangle. What is the maximum possible area X
of square?

ABC AB= 12, AC=15.

AB

YD CZ

(A) 100 (B) 64

(A) 1296 cm² (B) 25 cm² (C) 144 (D) 81
49
43. In the given figure area of isosceles right angle
(C) 1225 cm² (D) 1225 cm² triangle ABE is 72 cm2 and BE = AB and AB = 2
36 64 AD. AE||DC then what is the area of parallelo-
gram ADCE.

5

ABC O BC||DE, ADE
BE = AB, AB = 2AD, AE||DC
72 cm2 ADCF C
A
D E
O

A D 8 cm B

(A) 32+24 2 (B) 24+16 2

B EC (C) 24+32 2 (D) None of these

(A) 72 cm2 (B) 84 cm2 47. ABC is a right angle tr iangl e.
(C) 112 cm2 (D) 96 cm2
ABC=90°ACB=60° . If radius of smaller circle
is 2 cm. What is the radius of larger circle?

44. PQR is an equilateral triangle with side 12 cm. ABC ABC=90°ACB=60°|
S and T are mid point of side PQ and PR. What
is the area of shaded region?

PQR 12 ST
PQ
RS

(A) 4 (B) 6

(C) 4.5 (D) 7.5

48. There c(ri1r<crle2<sr3C) 1a,Cre2,Cp3lawcietdh arsadsihuoswrn1,ri2nagnidvern3
where

(A) 10 3 (B) 12 3 figure. What is the value of r2?

(C) 9 3 (D) 14 3 r1 r2 r3 C1, C2 C3
r2
r1<r2<r3

45. In the given figure, two square of sides 8 cm

and 20 cm are given. What is the area of shaded

part?

r2 r3
r1
C1 C2 C3

120 160 (A) r1 r3 (B) r1  r2
7 7 2
(A) (B)

180 240 (C) 2r1  r2 (D) r1  r3
7 13 r1  r2
(C) (D)
49. Let ABC be an isosceles triangle. Sappose that
the side AB and AC are equal and let the length
46. If O is the centre of circle and BC||DE. Find
perimeter of ADE. of AB and X cm. Let b denote the angle ABC

6

and sin b = 3/5. If the area of the triangle ABC (A) 1:2 (B) 1:4
is Msq cm, then which of the following is true
about M? (C) 2:3 (D) 4:9

ABC AB AC 52. In the diagram below CD = BF = 10 units and

AB x cm b, ABC CED = BAF = 30°. What would be the area of
ABC AED?
Sinb =3/5
M cm2 M CD = BF = 10 unit CED

(A) M  x2 (B) 3 M  x2 = BAF = 30°. AED
4 x2 A

(C) M  x 2 (D) x2 M x2 B
4 2 C

x2 3x 2 F
4 4
(E) M

50. PQR is a triangle and quadrilateral ABCD is E D
inscribed in it. QD=2cm, QC=5cm, CR=3 cm,
BR=4 cm, PB=6 cm, PA=5 cm, AD=3 cm. What  (A) 100  2  3  (B) 100 / 3  4
is the area of quadrilateral ABCD?  (C) 50 / 3  4  (D) 50 3  4

PQR CR=3 ABCD PB=6 QD=2
QC=5 BR=4 PA=5
AD=3 ABCD

(E) None of these
53. ABC and XYZ are equilateral triangle of 54

cm sides. All smaller triangles like ANM,
OCP, QPX, etc are also equilateral triangles.
Find the area of the shape MNOPQRM.

(A) 23 21 (B) 15 21 ABC XYZ
4 4 OPX
ANM, OCP,
17 23 MOPQRM
5 5
(C) 21 (D) 21

51. In the given figure, ST=8 cm, TU=9 cm, SU=12 A
cm, QU=24 cm SR=32 cm, PT=27 cm. What is
the ratio of area of PQR to area of PTR?fn M N Z
Y
ST=8 TU=9 SU=12
QU=24 SR=32 PT=27 | PQU RO
PTR

BQ PC

X

(A) 486 3 sq cm (B) 483 3 sq cm
(C) 386 3 sq cm (D) 386 3 sq cm

7

54. If diagonals of a rhombus are 12 cm and 16
cm, then what is the perimeter (in cm) of the
rhombus?

(A) 540 cm (B) 720 cm
17 17
(SSC CAPFs ASI & Delhi Police SI

Exam. 02.07.2017 (Ist Sitting) (C) 830 cm (D) 670 cm
(B) 40 17 17
(A) 20

(C) 60 (D) 80 61. What is the area of rhombus whose 3 vertex lie

55. If diagonals of a rhombus are 40 cm and 42 cm on circumference of circle and 4th vertex lie at
then what is the perimeter of the rhombus. the centre of circle of radius 16cm.

(A) 108 cm (B) 116 cm 16

(C) 120 cm (D) 82 cm (A) 144 3 cm2/ 2 (B) 128 3 cm2/ 2

56. The parimeter of a rhombus is 120 cm. If one (C) 112 3 cm2/ 2 (D) 160 3 cm2/ 2
of the diagonals be 48 cm what is the length of The base of a rhombus and a square is same. If
other diagonal. rhombus is inclined at an angle of 30º, then find
62. the ratio between area of square to area of
rhombus.
(A) 18 cm (B) 24 cm
30º
(C) 36 cm (D) 45 cm

57. If diagonals of a rhombus are 40 cm and 42 cm
then what is the area of Rhombus.

(A) 2:1 (B) 1:1

(A) 800 cm2 (B) 1200 cm2 (C) 2 :1 (D) 3 :1

(C) 1260 cm2 (D) 840 cm2 63. The perimeter of a rhombus is '2x' and its area
is y cm2. Find sum of the length of two diago-
58. The perimeter of a rhombus is 208 cm and one nals.
of its diagonal is 40 cm. Find its area-

'2x' 'y

cm2'

(A) 1920 cm2 (B) 1800 cm2 (A) x2  4y (B) x2  4y

(C) 1870 cm2 (D) 1824 cm2

59. If two diagonals of a rhombus are 24cm and (C) x 2  4y (D) x 2  4y

32cm. What is the ratio between its perimeter 64. Two adjacent sides of a prallelogram are 36cm
and its area. and 27cm. If distance between longer sides is
9cm. What is the distance between shorter side?
24 32

36 27
9
(A) 11:5 (B) 12:5

(C) 13:6 (D) 5:24

60. The perimeter of a rhombus is 204 cm and (A) 10cm (B) 12cm
length of one of its diagonal is 90 cm what is (C) 15cm (D) 14cm
the height of rhombus.

8

65. The adjacent sides of a parallelogram are in the 70. Diagonal of a square A is (a+b). What is the length

ratio 5:4 and its area is 326.50cm2. If distance of diagonal of a square whose area is thrice the

between shorter sides in 25cm. Find the distance area of square A.
between longer side.

A (a+b)

5:4 326.50 2 (A) 3(a+b) (B) 3 (a+b)
25

(A) 25cm (B) 20cm (C) 3 (a–b) (D) 3(a+b)2

71. Side of a square is 28 cm an circle is inscribed
in it. Find area of remaining portion of square
(C) 15cm (D) 28cm which is not enclosed by the circle.

66. Find area of a parallelogram whose adjacent
sides are 18 cm and 24 cm and one of the ver-
tex angle is 150.

(A) 134.4 cm2 (B) 164.28 cm2

(A) 192 cm2 (B) 216 cm2 (C) 153.2 cm2 (D) 168 cm2
(C) 256 cm2 (D) 228 cm2
72. Side of a square is 28 cm2 a cdircle is circum-
scribed to the square. Find area of the circle
67. Find area of a parallelogram whose two diago- which is not enclosed by the square.
nals are 24 cm and 36 cm and intersect each
other at an angle of 150°.

(A) 442.64 cm2 (B) 448 cm2

° (C) 462.36 cm2 (D) 452.24 cm2

73. If two diagonals of a rhombus are 24 cm and 32
cm. What is the ratio between its perimeter and
(A) 216 cm2 (B) 256 cm2 its area.
(C) 264 cm2 (D) 286 cm2
24 32
68. Ratio between sides/diagonal/perimeter of two
squares is 5:4. What is the ratio between area of (A) 11 : 5 (B) 12 : 5
two square?

5:4 (C) 13 : 6 (D) 5 : 24

74. ATS2hsiiqssupfarororecmeSes1dswibsiytchojosniitndiinenu2ge4.mFciimdndpaothsineectsouonfmdsoisdqf euaraSer2ae.
of infinitely many such square.
(A) 5:4 (B) 25:16

(C) 16:25 (D) 4:5

69. Area of a square A is 1526cm2 another square B S1
is formed such that the diagonal of square B is
(A) 1152 cm2 (B) 1108 cm2
3 times the diagonal of square A. What is the
area of square B ?

A 1526 2 B (C) 1156 cm2 (D) 1196 cm2
B B A3
75. AiooasfftsfhpSqoie2urr.rmdaiTmrseheqdeiSustba1epyrrwerjoiooStfchi3eninissisnisfdifgnoiesirmt3mce2ioledyndcptmsbioqny.iunuSjaoteeri.coenFo.finnisngdiddmsetqihSude1aptrsoheuienSmnt2

(A) 4608cm2 (B) 4398cm2 S1 S2 S1
(C) 4578cm2 (D) 4938cm2

9

S3
S2

   (A) 128 2 2 1
(B) 96 2 2  1 (A) 1/2 (B) 2/3

 (C) 114 2 2 1 (D) 128 2 (C) 1/4 (D) 3/4

80. Amit took 15sec to cross a rectangular park

76. Let S1 be a square of side 'a' another square S1 is diagonally walking at the rate of 68m/min while
pPfor1r,omPce2e,sdPs 3bc,yo..nj.o.t.iinnauirneegdp.meIrfiidmA1pe,toAei2nr,toAfo3sf.q.s.u.i.daaerreeSs2aSra1en,adSs2t,ahSni1ds, Anil took the same time to cross the same field
along its side walking at the rate of 92m/min.
What is the area of field.

P1  P2  P3...... 68
...... then the ratio A1  A2  A3...... .
15

S1 'a' S1 S2 92

S2 S3 P1 P2 P3 S1 (A) 105mt2 (B) 115mt2
S2 S1 S1
(C) 120mt2 (D) 135mt2
81.
P1  P2  P3...... A rectangular cardboad length and breadth are
A1  A2  A3...... . 24 cm and 18 cm. Fram the four corners of
the rectangle quarter circle of radius 3.5 cm
are cut. What is the perimeter of remaining
portion.

 2 1  2  2 2 – 2

(A) (B)
a a

 2 2  2  2 1  2 2 (A) 57 cm (B) 61 cm

(C) (D) (C) 78 cm (D) 70 cm
a a

77. Find area of largest circle that can be drawn 82. The length of two parallel sides of a trapezium
inside a rectangle with side 46 cm and 28 cm. are 18 m and 24 m. If its height is 12 m, what

is the area (in m2) of the trapezium?

(A) 624.2 cm2 (B) 618.2 cm2

(C) 632.2 cm2 (D) 616 cm2 (SSC CGL Tier-I CBE

78. Find area of a circle which is circumscribed to (Exam) 09.08.2017 (IInd Sitting)
a rectangle whose sides are 28 cm and 21 cm.

(A) 126 (B) 252

(C) 504 (D) 1024

(A) 962.5 cm2 (B) 932.5 cm2 83. In the given figure, PQRS is a trapezium in
which PM||SN, NR=9cm, PS=12 cm, QM=NR
(C) 918.5 cm2 (D) 926.5 cm2 and NR=SN. What is the area (in cm2) of
trapeztum?
79. Instead of walking along two adjacent sides of a
rectangular field, a boy took a short cut along PQRS
10 the diagonal and saved a distance half the longer MP||SN, NR = 9 cm, PS = 12 cm, QM = NR
side, then the ratio between shorter side to longer NR = SN.
side.

PS

QM NR

(SSC CHSL Tier-I CBE 1 (A)2 3 a² 1 (B)4 3 a²
(Exam) 08.08.2017 (IInd Sitting) 2 2

(A) 170 (B) 182  (C)12 3 a²  (D)14 3 a²
4 2

(C) 189 (D) 191 87. In the figure, ABCD is a square of side 14 cm.

84. Length of parallel sides of a trapezium are 46 E and F are mid points of side AB and CD. What
cm and 25 cm and non-parallel sides are 13 is the area of shaded region.

cm and 20 cm. Find area of trapezium. ABCD 14 AB

CD E F

(A) 414 cm2

(B) 446 cm2

(C) 434 cm2

(D) 426 cm2

85. PQ is the diameter of a semicircle and ABCD
is a square. What is the value of each side of
square. r is radius.

PQ ABCD (A) 108.5 (B) 94.5
r (C) 70 (D) 120

88. In the figure, PQRS is a square of side 8 cm.
PQO=60°. What is the area of triangle PQO?

PQRS PQO=60°
PQO

(A) 2r (B) 2r
3 5

(C) 2 r (D) 2r
3 3

86. ABCD is a square and ABEF is a rhombus (A) 32 3  (B) 24 3 1
 (D) 16 3  3
FEB=30°. Find the area of shaded region. If  (C) 48 3 1
side of square is "2a" cm.

ABCD ABEF 89. ABCD and BEFG are squares of side 8 cm and
6 cm. What is the area of shaded region?
FEB=30°
2a ABCD BEFG

11

DC

FG

A EB (A) 31.36 cm² (B) 125.44 cm²

(A) 14 (B) 12 (C) 62.72 cm² (D) 156.8 cm²

93. In the given figure, PQRS is a quadrilateral. If
(C) 16 (D) 8 QR=18 cm, and PS=9 cm, then what is the area
of quadrilateral PQRS?
90. In the figure, there is a rectangle at corner
10cm×20 cm. The corner A of rectangle is also
a point on circumference of circle. What is the PQRS QR=18
radius of circle? PS=9
PQRS

×20
A,

A

(A) 64 3 (B) 177 3
3 2
(A) 10 cm/ (B) 40 cm/
(C) 50 cm/ (D) None/ (C) 135 3 (D) 98 3
2 3

91. PQRS is a square of side 20 cm, SR is extended 94. The area of a regular hexagon of side 2 3 cm
to point T. If length of QT is 25 cm. What is
is:
the distance b/w centre O1 and O2.
3
PQRS SR T

QT O1 O2 (A) 18 3 cm2 (B) 12 3 cm2

(C) 36 3 cm2 (D) 27 3 cm2

95. What is the area (in sq cm.) of a regular hexa-
gon of side 14 cm?

(SSC CGL Tier-I CBE
(Exam) 19.08.2017 (IIIrd Sitting)

(A) 5 10 cm (B) 4 10 cm (A) 147 3 (B) 441 3

(C) 8 5 cm (D) 16 2 cm (C) 196 3 (D) 294 3

92. Radius of circle is 14 2 cm. PQRS is a square. 96. The ratio of the area of a regular hexagon and
an equilateral triangle having same perimeter
ABCD, EFGH, LMNO, WXZY are four identical is
square. What is the total area of all four circles?

14 2 PQRS

ABCD,EFGH, LMNO,WXZY (A) 2 : 3 (B) 6 : 1
(C) 3 : 2 (D) 1 : 6

12

97. Find the ratio between sides of an equilateral
triangle to side of regular hexagon inscribed in a
circle.

(A) 3 : 2

(B) 3 :1

(C) 2:1

(D) 3:1 (A) 24 3 (B) 18 3
98. An equilateral triangle side is 'a' cm. Its corners

cut away so as to form an regular hexagon, then (C) 72 3 (D) 36 3
find the ratio between area of hexagon to area of

remaining part of equilateral triangle. 101. ABCDEF is a regular hexagon of side 12 cm,

4 P,Q, and R are mid point of side AB,CD and
EF. What is the area of triangle?

ABCDEF 12 P,Q
R AB,CD
EF

(A) 2 : 1

(B) 3 : 2

(C) 1 : 2

(D) 2 : 3

99. ABCDEF are hexagon with equal sides all the (A) 27 6 (B) 81 3
circles are of same radius 'r' with each vertex

of hexagon as centre are drawn. Find the area (C) 54 3 (D) 54 6
of shaded region.
102. PQRSTU is a regular hexagon of side 12 cm.

ABCDEF What is the area of triangle SQU (in cm²)?

r PQRSTU,12

SQU

(A) r² (B) 2r² (A) 162 3 (B) 216 3

(C) 3 r² (D) 5 r² (C) 108 3 (D) 54 3
2 4
103. ABCD is a regular hexagon of side 12 cm. what

100. ABCD is a regular hexagon whose side is 6 cm. is the area of shaded region?
APF, QAB, DCR and DES are equilateral tri-
angle. What is the area of shaded region. ABCD

ABCD DES
APF,QAB,DCR

13

(A) 54 3 cm² (B) 36 3 cm² 108. Ratio between radius/diameter/circumference of
two circles is 5:4. What is the ratio between area
(C) 48 3 cm² (D) 52 3 cm² of two circles?

104. Find area of a octagon whose perimeter is equal 5:4
to 16 cm.

(A) 5:4 (B) 25:16

   (A) 12 2 1 cm2 (B) 16 2 1 cm2 (C) 16:25 (D) 4:5

   (C) 8 2  1 cm2 (D) 8 2 1 cm2 109. The perimeter (in metres) of a semicircle is
numerically equal to its area (in square metres).
Perimeter of a regular octagon and regular
105. hexagon is equal. What is the ratio between area The length of its diameter is (Take = 22 )
of octagon to area of hexagon. 7

(A) 3 6 metres (B) 5 6 metres
11 11

(A) ( 3 + 2 ):4 (B) ( 3 +1): 6 (C) 6 6 metres (D) 6 2 metres
11 11
(C) ( 6 + 3 ): 5 (D) ( 6 + 3 ):4
110. The difference of perimeter and diameter of a
106. A square whose side is 2m, has its corners cut circle is X unit. The diameter of the circle is
away so as to form an octagon will all sides equal,
then the length of each side of octagon is- X

2

(A) X unit (B) X unit
 1  1

(A) 2 (B) 2 X (D) X  1 unit
2 1 2 1 (C) 1 unit

2 (D) 2 111. If the perimeter of circle A is equal to perim-
(C) 2 – 1 2 –1 112. eter of semi circle B, what is the ratio of their
113. areas?

107. ABCD is a rectangle of side 15 cm and 7cm AB
and MNOP is a ellipse inscribed in the rect-
angle. Find area of shaded region. (A)  22 : 22 (B) 22 :  22

ABCD 15

MNOP (C)  22 : 42 (D) 42 :  22

Area of a circle is increased by 22cm, If its radius
is increased by 1cm. What is the original radius
of circle.

22
1

(A) 3cm (B) 6cm

(A) 1 2  105 (B) 1 4 105 (C) 4.5cm (D) 1.5cm
(D) 1  4   60
(C) 1 4 105 If the area of a circle is A, radius of the circle
is r and circumference of it is C, then
14
Ar
C

(SSC CGL Tier-I Exam, 09.08.2015 C1
(1st Sitting) TF No. 1443088) C2

(A) A C (B) rC  2A
r
(SSC CGL Tier-I Exam, 16.08.2015
(C) C  r (D) AC  r2 (1st Sitting) TF No. 3196279)
A 2 4
9 4
114. Three coins of the same size (radius 1 cm) are (A) 25 (B) 25
placed on a table such that each of them
touches the other two. The area enclosed by (C) 9 (D) 16
the coins is 16 25

118. A circular road runs around a circular ground.
If the difference between the circumference
of the outer circle and the inner circle is 66

(A)  π  3  cm2  3  π  cm2 metres, the width of the road is: (Take = 22 )
 2  (B)  2  7

(C) 2 3  π  cm2 (D) 3 3  π  cm2
2  2 

115. Three circles of radius a, b, c touch cach other (A) 10.5 metres (B) 7 metres
extemally. The area of the triangle formed by
joining their centre is (C) 5.25 metres (D) 21 metres

a, b, c 119. The external fencing of a circular path around
a circular plot of land is 33 m more than its
(A) 1b c abc interior fencing. The width of the path around
the plot is

(B) a b c  ab 

(C) ab + bc + ca (A) 5.52 m (B) 5.25 m
(D) None of the above
(C) 2.55 m (D) 2.25 m
116. ABC is an equilateral triangle of side 2cm, with
A, B, C as centres and radius is 1 cm three circle 120. The ratio of the outer and the inner perimeter
are drawn. The area of region within the triangle of a circular path is 23 : 22. If the path is 5
bounded by three circle are. metres wide, the diameter of the inner circle
is:
ABC 2 ABC
1

 3 3 –   3 –   (A) 110 m (B) 55 m
 2   2 
(A) cm2 (B) cm2 (C) 220 m (D) 230 m

121. A 7 m wide road runs outside around a circu-
lar park, whose circumference is 176 m. The
(C)  3 –  cm2 (D)   – 3  cm2
 2   2  22
area of the road is: (use π  7 )

117. LciertcCle1saonfdaCt2rbiaentghlee inscribed and cirumscribed
with sides 3 cm, 4 cm and
15
5 cm them area of C1 is (A) 1386 m2 (B) 1472 m2
area of C2 (C) 1512 m2 (D) 1760 m2

C1 C2

122. A person observed that he required 30 sec less (A) 350 m2 (B) 196 m2
time to cross a circular ground along its diameter
than to cover it along its boundary. If his speed (C) 154 m2 (D) 22 m2
is 1.8 km/h. What is the circumference of circle
? 127. At each corner of a triangular field of sides 26
m, 28 m and 30 m, a cow is tethered by a rope
30 1.8 of length 7 m. The area (in m) ungrazed by the
cows is

26 m, 28 m, 30 m

(A) 22mt (B) 15mt

(C) 18mt (D) 15.4mt (A) 336 (B) 259
(C) 154 (D) 77
123. A wire when bent in the form of a square enclose
124. an area of 484cm2. If same wire bent in the form 128. Amit took 15sec to cross a rectangular park
125. of a circle then find area of a circle. 129. diagonally walking at the rate of 68m/min while
126. 130. Anil took the same time to cross the same field
484 along its side walking at the rate of 92m/min.
What is the area of field.

(A) 616cm2 (B) 484cm2 68
15
(C) 528cm2 (D) 576cm2

A wire bent in the form of an equilateral triangle 92

enclose an area 121 3 cm2. If same wire is bent (A) 105mt2 (B) 115mt2
in the form of a circle then find area of circle.

121 3 2 (C) 120mt2 (D) 135mt2

(A) 346.5cm2 (B) 324.6cm2 LdlaPiinnei1naf,t.eimrPLCPi1eet0etbtPBeeCc2r.,i1aPr,oac2cCfnliie2Crsd,.ctCIlsPhefu32eAp.w.PmBp.i.3to..i=h.ds.Fe3ccpi0ienoPrnid1ccntlmiretsseuo.wtmfPhilt0eihnaomnefddiPiaad1rmAeBpBaeoatiioensnfrdttPahso0loefl,

(C) 352.6cm2 (D) 352.5cm2

The length of circumference of a circle is equal C P0 C AB
the perimeter of a triangle of equal sides and P1, P0 B P2, P1 B P0,
also the perimeter of a square. The area covered C1, C2, C3 ..........
by circle, triangle and square are C, T and S
respectively. Then-

P1, P1 P2, P2 P3.

AB = 30 cm

C, T S (A) 292 cm2 (B) 340 cm2

(A) S>T>C (B) C>T>S (C) 300 cm2 (D) 168 cm2

(C) C>S>T (D) S>C>T LoldineinatemiCnPe0btfBeeiPnra2ioticefsilCrytc.hlseeFuipwmnpiditodhssepucoemPinn1 ttoirsefotfpPhle0eirnaimenmdiPed1tABepBroaiinosnfdttahsoloefl
circles of AB = 72 cm.
A cow is tied on the corner of a rectangular
filed of size 30 m × 20 m by a 14 m long rope.
The area of the region, the she can graze, is

(use π  22 ): C P0 AB, C P1, P0
7
B P2 P1 B
30 m × 20 m AB = 72 cm.

22 (A) 176 cm (B) 144 cm
7
( π  ) (C) 192.25 cm (D) 232.5 cm

16

131. O is the centre of circle and AOB=150° and S1 'a' S1 S2
S1
the shaded portion is x part of circular region S2 S3 P1 P2 P3 S1
then x=? S2 S1

O AOB=150° P1  P2  P3......
x x=? A1  A2  A3...... .

 2 1  2  2 2 – 2

(A) (B)
a a

(A) 1 (B) 1  2 2  2  2 1  2 2
12 9
(C) (D)
1 1 a a
6 4
(C) (D) 135. Radius of larger circles is 'R'. each of radius of
inner circle is 'r', r = ?
132. PQ is the diameter of a semicircle and ABCD
is a square. What is the value of each side of
square. r is radius. R rr
=?
PQ ABCD
r

(A) R( 2  1) (B) R( 2  1)

(C) R(2  2) (D) R( 3  2)

(A) 2r (B) 2r 136. Radius of larger circle is "R" cm another circle
3 5 "r" cm is also placed as shown in figure. What
is the value of "r".
2 2r
(C) 3 r (D) 3 "e" "r"
R
133. Find ratio between sides of two square. if one
square is inscribed in a circle and second square
is inscribed in semicircle of same radius-

(A) 5 : 2 (B) 3 : 2  2 1  2 1
 (A) R 2 1  (B) R 2  1
(C) 2:1 (D) 5 : 3
 3 1  3  1
134. Let S1 be a square of side 'a' another square S1 is  (C) R 3  1  (D) R 3  1
formed bcyonjotiinnuinegd.mIfidA1p,oAi2n,tAo3 f..s..i.daereS2araenads this
17 process and 137. AB is the diameter of circle and O is the cen-
tre of largest circle. AO and BO are the diam-
P1, P2, P3, ..... are perimeter of squares S1, S2, S1, eter of two circle. R is the centre of circle which
touches three given circle. Find radius of circle
P1  P2  P3...... R. If radius of largest circle is "2 cm".
...... then the ratio A1  A2  A3...... .

AB O AO 140. PQRS is diameter of circle of radius 6 cm.
BO R PQ=QR=RS. Find ratio between area of shaded
region to unshaded region.
R
PQRS

PQ=QR=RS

(A) 1 cm (B) 2 cm
3 3
(A) 1 : 2 (B) 5 : 13

(C) 2 cm (D) 3 cm (C) 5 : 18 (D) 2 : 7
5 4
141. AD is the diameter of circle. AB=BC=CD. Find
138. Three horses are tired at point P, Q and R ratio between area of shaded region to whole
horses. Tied at P and Q can graze within the circle.
semicircle and horse tied at R can graze within
the circle. O is the centre of semicircle. What AD AB=BC=CD
% of area of garden that can not be grazed by
horses (appor).

P, Q R
R
PQ
O

(A) 1:3 (B) 2:3

(C) 1:2 (D) 1:4

142. ABCD passes through centre of each circle.
AB=2, CD=1. If area of middle circle is the av-
erage of area of other two circle. What is the
length of BC.

(A) 20 (B) 28 ABCD AB=2,CD=1,|

(C) 36 (D) 40 BC

139. In the given figure, AB,AE,EF,FG and GB are
semicircles AB=56 cm, AE=EF=FG=GB. What
is the area of shaded region.

AB,AE,EF,FG GB
AE=EF=FG=GB|
AB=56

(A) 6 1 (B) 6 1

(C) 6  3 (D) 6 1

143. PQR is a quadrant of radius 7 cm. Circle is
inscribed in the quadrant. What is the area of
(A) 414.46 cm² (B) 382.82 cm² circle?
(C) 406.48 cm² (D) 394.24 cm²
PQR,7
18

148. The cost of levelling a circular field at 50 paise
per square metre is Rs. 7700. The cost (in Rs.
) of putting up a fence all round it at Rs. 1.20

per metre is (Use π  22 )
7

(A) 385–221 2 (B) 154–77 2

(C) 308–154 2 (D) 462–308 2

144. A street of width 10 metres was rounds from (SSC CGL Tier-II (CBE)
145. outside a rectangular garden whose measure-
146. ments is 200 m × 180 m. The area of the path Exam. 12.01.2017)
(in square metres) is
(A) Rs. 132 (B) Rs. 264

(C) Rs. 528 (D) Rs. 1056

× 149. The outer circumference of a circular race-
150. track is 528 metre. The track is everywhere
(A) 8000 (B) 7000 14 metre wide. Cost of levelling the track at
the rate of Rs. 10 per sq. metre is:

(C) 7500 (D) 8200

The length and breadth of a rectangular field (SSC CHSL (10+2) LDC, DEO
are in the ratio 7 : 4. A path 4 m wide running
all around outside has an area of 416 m2. The
breadth (in m) of the field is

& PA/SA Exam. 06.12.2015

(IInd Sitting) TF NO. 3441135)

(A) 28 (B) 14 (A) Rs. 77660 (B) Rs. 66760

(C) 15 (D) 16 (C) Rs. 76760 (D) Rs. 67760

A rectangular park 60 metre long and 40 metre The floor of a corridor is 100 m long and 3 m
wide has two concrete crossroads running in wide. Cost of covering the floor with carpet 50
the middle of the park and rest of the park has cm wide at the rate of Rs. 15 per m is
been used as a lown. If the area of the lawn is
2109 metre2 then the width of the road is

(A) Rs. 4500 (B) Rs. 9000
(C) Rs. 7500 (D) Rs. 1900

(A) 3 metre (B) 5 metre 151. The cost of fencing around a rectangular field at
the rate of Rs.125 per foot is Rs.13500. What
(C) 6 metre (D) 2 metre would be the cost of flooring the field at the rate
of Rs.75/ft2 if length of field is 5/4 times of its
147. Three sides of a triangular field are of length breath.
15 m, 20 m and 25 m long respectively. Find
the cost of sowing seeds in the field at the rate
of 5 rupees per sq. m.

/ft2

(A) Rs. 300 (B) Rs. 600 (A) Rs.52000 (B) Rs.54000
(C) Rs. 750 (D) Rs. 150 (C) Rs.53500 (D) Rs.48600

19

152. Find the length of band. If radius of each circle  (A) 2 3 1 R  (B) 2 3 3 1 R
is R.

   R
(C) 3 3 1 R (D) 3 2 1 R

156. ABCP is a quadrant of circle of radius 14 cm
with AC as diameter a semicircle is drawn. Find
the area of shaded region-

ABCP,14 AC

(A) 2R + 2R (B) 2R + 4R

(C) 2R + 6R (D) 2R + 8R

153. Find the length of rubber bond. If radius of
each circle is 'r'.

r

(A) 49 cm² (B) 98 cm²

(C) 126 cm² (D) 148 cm²

157. In the given figure, ABC is right angle triangle
in which C is right angle three semicircle are
(A) 2r (+4) (B) 2r(+5) drawn on diameter AB,BC and AC. The area of

ABC is 48 cm². Find area of shaded region.

(C) 2r (+10) (D) 2r(–5) ABC C
AB,BC
154. Find the length of rubber band. If radius of AC
each circle is 2 cm. 48
ABC

(A) (25–22) cm² (B) (37–11) cm²

(C) (48–48) cm² (D) 48 cm²

 (A) 2 3 3  1 R  (B) 2 3 3  1 R 158. ABCD is a square of side 'a' cm. AB,BC,CD and
DA are diameter of four semicircles. What is
the area of shaded region.

 (C) 2 3 2  1 R  (D) 3 3 3  1 R ABCD 'a' AB,BC,CD DA

155. Find the length of side of triangle. Radius of
each circle is "R".

'R'

(A) 2 – a² (B) ( a²)
(C) 4 – a² (D) a²

20

159. ABC is a right angle triangle. AB=15 cm, (A) 32 3a²   3 
AC=8cm three semicircle are drawn with di-  2 
ameter BC,BC,AB. Find the area of shaded re- (B) a²
gion.

ABC AB=15 AC=8 (C)  3 a²  (D) 3 3 a ² 
AB  4  2 
BC,AC

162. In the figure, ABCD is a square with side 20 cm.
Two circle are drawn with radius AB and CD tak-
ing centre B and D. What is the area of shaded
region?

ABCD 20 B
D AB

CD

(A) (48–16) cm² (B) (32–7) cm²

(C) 55 cm² (D) 60 cm²

160. In the given figure, 3 semicircles are drawn on

three sides of ABC. AB=21, BC=28, CA=35.

Find area of shaded region.

ABC (A) (50–100) cm²

AB=21,BC=28,CA=35 (B) (100–200) cm²

(C) (200 – 400) cm²

(D) 400 cm²

163. ABCD is a square. Four equal semicircles are
drawn in such a way they meet each other at
point O. AB, BC, CD and DA are diameter of
four semicircles. Find area of shaded region. If
side of square is 4 cm.

ABCD

O AB, BC, CD DA

(A) 588 (B) 324

(C) 294 (D) 286

161. In the figure, ABCDEF is regular hexagon of side
''a'' cm. A circle is circumscribed to hexagon. 6
semicircles are drawn on diameter
AB,CD,EF,AF,BC,DE. Find the area of shaded
region.

a (A) 8(–2) cm² (B) 32 (–2) cm²
AF, BC,DE
AB, CD, EF, (C) 8 2  2cm² (D) 32 2  2 cm²

164. ABCD is a square and M,N,O,P are the mid point
of side of square. Taking AM, BM, BN, NC, CO,
OD, DP, PA is diameter. Semicircles are drawn.
Find area of shaded region. If side of square is
4 cm.

ABCD M,N,O,P

AM, BM, BN, NC, CO, OD, DP, PA

21

XA=7

(A) 2(+2) cm² (B) 2(–2) cm²

(C) 4(+2) cm² (D) 2(+8) cm² (A) 70 (B) 140
(C) 77 (D) 84
165. In the figure, four identical semicircles are drawn
in a quadrant. XA=cm. What is the area of shaded
region.

ANSWER KEY

1. (B) 18. (B) 35. (C) 52. (D) 69. (C) 86. (B) 103.(A) 120.(C) 137.(B) 154.(B)
2. (C) 19. (C) 36. (C) 53. (A) 70. (B) 87. (B) 104.(D) 121.(A) 138.(B) 155.(B)
3. (B) 20. (A) 37. (D) 54. (B) 71. (D) 88. (A) 105.(D) 122.(B) 139.(D) 156.(B)
4. (C) 21. (C) 38. (B) 55. (B) 72. (B) 89. (B) 106.(B) 123. (A) 140.(D) 157.(D)
5. (C) 22. (C) 39. (D) 56. (C) 73. (D) 90. (C) 107.(C) 124. (A) 141.(A) 158.(D)
6. (C) 23. (B) 40. (A) 57. (D) 74. (A) 91. (A) 108.(B) 125.(C) 142. (A) 159.(D)
7. (D) 24. (A) 41. (A) 58. (A) 75. (A) 92. (B) 109.(C) 126.(C) 143.(D) 160.(C)
8. (C) 25. (C) 42. (C) 59. (D) 76. (*) 93. (C) 110.(A) 127.(B) 144. (A) 161.(D)
9. (C) 26. (C) 43. (A) 60. (B) 77. (D) 94. (A) 111.(A) 128.(C) 145.(D) 162.(C)
10. (D) 27. (A) 44. (B) 61. (B) 78. (A) 95. (D) 112.(A) 129.(C) 146.(A) 163.(A)
11. (D) 28. (B) 45. (B) 62. (A) 79. (D) 96. (C) 113.(B) 130.(B) 147.(C) 164.(A)
12. (A) 29. (D) 46. (D) 63. (C) 80. (C) 97. (B) 114.(B) 131.(C) 148.(C) 165.(D)
13. (C) 30. (A) 47. (B) 64. (B) 81. (C) 98. (A) 115.(D) 132. (A) 149.(D)
14. (B) 31. (A) 48. (A) 65. (B) 82. (B) 99. (B) 116.(B) 133. (A) 150.(B)
15. (C) 32. (C) 49. (D) 66. (B) 83. (C) 100.(C) 117.(B) 134. (*) 151.(D)
16. (B) 33. (D) 50. (C) 67. (A) 84. (D) 101.(B) 118.(A) 135.(B) 152.(C)
17. (A) 34. (A) 51. (D) 68. (B) 85. (D) 102.(C) 119.(B) 136.(A) 153.(B)

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