Sheet MENSURATION – 2D

10
– 2D
13. In the given figure, ABCDEF is a regular hexa- E D
gon whose side is 6 cm. APF, QAB, DCR and
DES are equilateral triangles . What is the area
(in cm².) of the shaded region?
ABCDEF
APF QAB DCR DES
2 F C

(a) 24 3 (b) 18 3

(c) 72 3 (d) 36 3
P Q
A B
A 15. Find the ratio of shaded area to unshaded area?

F B
1 1 1 1
(a) (b) (c) (d)
8 9 10 12

16. ABCDEF is a regular hexagon whose area is

E C
180cm2. Find the area of shaded region?

ABCDEF 180cm2
D

S R (a) 9 cm² (b) 10 cm²

14. ABCDEF is a regular hexagon, find the ratio of
the area of shaded region to area of hexagon (c) 12 cm² (d) 15 cm²
ABCDEF?/ABCDEF E D
ABCDEF

1 3 2 1
(a) (b) (c) (d)
3 10 5 2
F C

A B
17. ABCDEF is a regular hexagon, shaded area is what
percent of regular hexagon?
ABCDEF

FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 1

 (a) 11.11% (b) 12.5% (c) 9.09% (d) 10%

1
E D
3

(a) 66.66% (b) 33.33%

(c) 83.33% (d) 56.41%
20. A square and a regular hexagon are drawn such
F C that al the vertices of the square and the hexagon
are on a circle of radius r cm. The ratio of area of
the square and the hexagon is:

A B
(a) 1 : 2 (b) 2 : 3
18. ABCDEF is a hexagon with side 8cm each, find (c) 3 : 4 (d) 4 : 3 3
the area of shaded region?
ABCDEF

80 64
(a) (b)
3 3

93
(c) (d) 40 30
3

P 21. ABCDEF is a regular hexagon and M and N are

the mid points of opposite edges as shown in the
figure. If the area of the hexagon is 120 units.
F Q Then what is the product of the lengths of AD and
MN?/ABCDEF M N

AD MN

T R
(a) 160 (b) 200 (c) 100 (d) 140

19. An equilateral triangle of area 300 cm² is cut from

its three vertices to form a regular hexagon. Area
of hexagon is what percent of the area of triangle?
1
(Each side of the regular hexagon is rd the origi-
3
nal side of equilateral triangle )

2 FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA

 B M C 24
(a) 4.8 cm (b) cm (c) 5.8 cm (d) 12 cm
7
A

6
A D

8
F N E
22. In the given circle, there are an equilateral tri-
angle and a regular hexagon. If the lengths of their
sides are a and b respectively, then which one of B C
the following is correct? 2. In the following figure ABC is a right angle tri-
angle. A square is made in this triangle, if AF = 16
cm, and CD = 9 cm. Find the area of square
a b BDEF?
ABC
(a) a² = 2b² (b) b² = 3a² AF = 16 CD = 9
(c) b² = 2a² (d) a² = 3b² BDEF
(a) 144 cm² (b) 64 cm²
(c) 16 cm² (d) 81 cm²

3. In the following figure ABC is a right angle tri-

1. If area of regular octagon is 18  2 1  find its angle. A square is made in this triangle, if AB = 5
cm, and BC = 12 cm. Find the area of square.
side:/ 18  2 1  ABC
AB = 5 BC = 12
(a) 3 (b) 4 (c) 5 (d) 1
1. ABC is a right angle triangle right angle at B if a
square is drawn in right angle triangle such that its 132 451
(a) 12 cm² (b) 21 cm²
one vertex lie on AC. If AE = 6 cm and EC = 8 cm. 289 289
Then find the side of square./ABC
51 2
B (c) 31 cm² (d) 21 cm²
289 289
AC AE = 6
EC = 8

FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 3

 A 6. In the following figure ABC is a right angle tri-
angle. A square is made in this triangle, if AC = 5
cm, BC = 4 and AB = 3 cm. Find the side of square.
ABC
AC = 5 BC = 4 AB
5
=3

90 60
(a) cm (b) cm
37 37

B C 12 19
12 (c)
5
cm (d)
47
cm
4. In the following figure ABC is a right angle tri-
angle. A square is made in this triangle, if AP = 4 A
cm, and MC = 3 cm. Find the area of square.
ABC
AP = 4 MC = 3
5

(a) 5.76 cm² (b) 6.76 cm²

3

(c) 25 cm² (d) 6.35 cm²

A

B M C
4
4 O 1. The area of the largest triangle that can be in-
scribed in a semicircle of radius 6 m is.

P N
(a) 36 m² (b) 72 m² (c) 18 m² (d) 12 m²
2. Find the area of the largest possible triangle that
can be placed inside a semicircle of radius 10
B M 3 C cm./
5. In the following figure ABC is a right angle tri-
angle. A square is made in this triangle, if AO =
(a) 75 cm² (b) 25 cm²
12 cm, and MC = 27 cm. Find the side of square.
(c) 50 cm² (d) 100 cm²
ABC 3. The area of the largest triangle that can be in-
AO = 12 MC = 27 scribed in a semicircle of radius 4 cm in square
cm is-/
2

(a) 9 cm (b) 18 cm (c) 21 cm (d) 12 cm (a) 16 cm² (b) 14 cm²

A (c) 12 cm² (d) 18 cm²
1. A right angled isosceles triangle is inscribed in a
12 semi-circle of radius 7 cm. The area enclosed by
the semi-circle but exterior to the triangle is:
O
4 FOLLOW RAKESH YADAV SIR ON SOCIAL
cm MEDIA

P N

27
 3. Find the area of the shaded region in, if PQ = 24
cm, PR = 7 cm and O is the centre of the circle./
(a) 18 cm² (b) 28 cm² PQ = 24 PR =
(c) 25 cm² (d) 15 cm² 7 O
4327 4523
(a) cm² (b) cm²
28 28

4529 4129
(c) cm² (d) cm²
28 28

Q
2. O is the centre of a circular arc and AOB is a
straight line. Find the perimeter and the area of
the shaded region correct to one decimal place.
(take  = 3.142) O
24
O AOB
25
 = 3.142

(a) 59. 4 cm, 61.1 cm² R P

7
(b) 51. 4 cm, 69.1 cm²
(c) 61. 4 cm, 59.1 cm²
(d) 69. 4 cm, 51.1 cm²
C

16
cm

cm
12

A O B

FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 5