Sheet MENSURATION – 2D

01
– 2D
the perimeter is 72 cm. The sides are:

Scalene Triangle
(a) 24, 16, 32 (b) 48, 24, 12
1. The area of a triangle whose sides are 15m, 16m (c) 36, 24, 12 (d) 36, 18, 9
and 17 m is: 7. The sides of a triangular park are 60 m, 112 m
and 164 m. The cost of leveling the park at the
rate of Rs. 8.50 m2 is:/

(a) 23 21 m2 (b) 24 21 m2
(a) 18,316 (b) 17,136
(c) 28 23 m2 (d) 26 19 m2
(c) 18,164 (d) 17,085
2. If the area of a triangle is 250 m2 and base : height 8. The sides of a triangular park are in the ratio 12 :
is 4 : 5, find its height : 17 : 25 and perimeter is 1080 m. The area (in
=4: hectares) of the park is …../
5
(a) 15 m (b) 35 m (c) 25 m (d) 5 m
3. What is the area of a triangle having perimeter (a) 4.5 (b) 3.6 (c) 4.8 (d) 4.2
32cm, one side 11cm and difference of other two 9. It is given that the area of a triangle is A. The val-
sides 5cm?/ ues of its perimeter, in radius, circumradius and
the average of the lengths of the medians are re-
spectively, p ,q, R and d. The ratio of A : p is equal
(a) 5 30 cm2 (b) 7 35 cm2 to :
A
(c) 8 30 cm 2
(d) 9 26 cm 2
p, q,
4. The area of a triangle is 15 sq cm and the radius of R d A:p
its encircle is 3 cm. Its perimeter is equal to:/ (a) (R + r) : d
2
(b) r : 2
(c) r : 1 (d) (R - r)2 : r
10. The area of a triangle is 96 cm2 and the length of
(a) 12 cm (b) 20 cm one of its sides is 24 cm. What is the length of the
perpendicular drawn to this side of the triangle from
(c) 5 cm (d) 10 cm
the opposite vertex ?
5. One side of a triangle is 7 with its perimeter equal

to 18 and area is equal to 108 then the other

two sides are: /
(a) 16 cm (b) 8 cm
108
(c) 4 cm (d) 12 cm
11. If the three sides of a triangle are 11 cm, 12 cm
(a) 6 & 5 (b) 3.5 & 7.5 (c) 7 & 4 (d) 3 & 8 and 13 cm, then what is the area of the given tri-
6. The sides of a triangle are in the ratio 3 : 2 : 4 and angle (in cm2)?/

FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 1

 more than half of the third side. The area of the
triangle is.

(a) 15 13 (b) 13 26

(c) 6 105 (d) 17 42 (a) 64 3 cm2 (c) 48 3 cm2

12. What is the area of a triangle whose sides mea-
sure 5 cm, 6 cm and 7 cm ? (c) 36 3 cm2 (d) 72 3 cm2
Equilateral Triangle
(a) 10,9797 cm3 (b) 12.8484 cm3
(c) 16.4645 cm3 (d) 14.6969 cm3 1. The area of a field in the shape of a triangle with
13. The base of triangle is 8.5 cm and height is 14 cm. each side x metres is equal to the area of another
Find the having of another triangle, having base triangular field having sides 50 m, 70 m and 80
14 cm and double the area of the first triangle is: m. The value of x is closet to:
x

x
(a) 66.5 (b) 63.2 (c) 62.4 (d) 61.8
(a) 17 cm (b) 15 cm
(c) 16 cm (d) 14 cm 2. If the area of an equilateral triangle is 36 3 cm2,
14. What is the area (in cm2, correct to one decimal then the perimeter of the triangle is:
place) of a triangle whose base is 21.4 cm and
height is 15.5 cm? 36 3

(a) 36 3 cm (b) 36 cm
(a) 165.9 (b) 156.6
(c) 165.6 (d) 156.9
(c) 18 3 cm (d) 12 cm
3. The area of a table top in the shape on an equilat-
1 1 1 eral triangle is
15. The base of a triangle are in the ratio : : 9 3 cm2, What is the length (in
3 5 4 cm) of each side of the table ?/
and its perimeter is 141 cm. The difference be-
tween the greatest side and the smallest side is: 9 3

1 1 1 (a) 6 (b) 2 (c) 4 (d) 3

: :
3 5 4 4. What is the height (in cm) of an equilateral tri-
angle whose each side is 8 cm ?

(a) 18 cm (b) 15 cm
(c) 12 cm (d) 24 cm (a) 4 3 (b) 3 2
16. The length of the base of a triangle is 3 cm smaller
than the length of its altitude. Its area is 104 cm2. (c) 4 2 (d) 3 5
What is the length of the base ?
5. If the height of an equilateral triangle is 10 3 cm,
the area is:
(a) 13 cm (b) 12 cm 10 3
(c) 14 cm (d) 11 cm
17. In a triangle, the average of any two sides is 6 cm (a) 124 3cm 2 (b) 75 3cm 2

2 FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA

 (c) 83 3cm 2 (d) 100 3cm 2 36 3 ABC
6. A circle is inscribed in a equilateral triangle of side
24 cm. What is the area (in cm2) of a square in-
(a) 2 3 (b) 3 3
scribed in the circle ?/
(c) 4 3 (d) 6 3

(a) 48 (b) 72 (c) 96 (d) 54 13. ΔABC is a equilateral triangle find the ratio of
7. Twelve sticks, each of length one unit, are used to radius of incircle and circuimcircle of this equi-
form an equilateral triangle. The area of the tri- lateral triangle.
angle is: / ΔABC

(a) 1 : 2 (b) 1 : 4 (c) 2 : 1 (d) 4 : 1

(a) 3 3 sq. units (b) 2 3 sq. units
14. ΔABC is a equilateral triangle find the ratio of
(c) 4 3 sq. units (d) 8 3 sq. units area of incircle and circuimcircle of this equilat-
8. What is the perimeter (in cm) of an equilateral tri- eral triangle./ ΔABC
angle whose heights is 3.46 cm ?
(a) 1 : 2 (b) 1 : 4 (c) 2 : 1 (d) 4 : 1
15. ΔABC is a equilateral triangle find the ratio of
(a) 10.4 (b) 9 (c) 6 (d) 12 side of equilateral triangle and radius of incircle.
9. The sum of all the three sides of an equilat-
ΔABC
eral triangle is 15 3 cm. The height of the tri-
angle is: cm./
(a) 2 : 1 (b) 2 3 :1
15 3
(a) 7 cm (b) 8 cm (c) 7.5 cm (d) 9 cm (c) 1: 2 3 (d) 3 :1
16. ΔABC is a equilateral triangle find the ratio of
10. The area of an equilateral triangle is 10. 24 3 m2.
side of equilateral triangle and radius of circum-
Its perimeter (in m) is: circle.
10. 24 3 m2 ΔABC

(a) 3.2 (b) 9.6 (c) 6.4 (d) 19.2

(a) 1: 3 (b) 2 3 :1
11. The perimeter of an equilateral triangle is 75 cm.
Find its area. (c) (d)
1: 2 3 3 :1
Isosceles right triangle

625 2 625 3 1. In an isosceles triangle ABC with AB = AC and AD

(a) cm2 (b) cm2
4 4 is perpendicular to BC, if AD = 6 cm and the pe-
rimeter of  ABC is 36 cm, then the area of
625 3 125 3 ABC is:
(c) cm3 (d) cm3
3 4  ABC AB = AC AD, BC
12. ABC is a quadrilateral. If the area of the triangle AD = 6  ABC 36
 ABC
is 36 3 , then what is the radius of circle, cir-
cumscribing the triangle ABC ?/ABC (a) 45 cm² (b) 48 cm²

FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA 3

 (c) 54 cm² (d) 64 cm²
2. The base of an isosceles triangle is 6 cm and its
(a) 23 cm (b) 22 cm
perimeter is 16 cm. Its are is:
(c) 21 cm (d) 20 cm
7. The length of each equal side of and isosceles
triangle is 15 cm and the included angle between
(a) 11 cm² (b) 12 cm² those two sides is 90°. Find the area of the tri-
angle.
(c) 9 cm² (d) 10 cm²
3. The perimeter of an isosceles triangle is 3.6 m and
its base is 30 cm shorter than each of the equal °
sides. What is the area (in m²) of the triangle ?

225
² (a) cm² (b) 225 cm²
2

(a) 0.6 (b) 0.72 (c) 0.54 (d) 0.08 255 125
(c) cm² (d) cm²
4. The perimeter of an isosceles triangle is 91 cm
2 2
8. The perimeter of an isosceles right triangle is
1
16 
and its base is 1 times each of its base is. What
4 2 + 16 cm, then the area of the triangle
is the length (in cm) of its base ?/
is:

1
16 2 + 16 
4 (a) 64 sq. cm (b) 76 sq. cm
(c) 66 sq. cm (d) 58 sq. cm
(a) 35 (b) 20 (c) 25 (d) 28 9. The perimeter of an isosceles right triangle having
area 100 cm² is:
5. In an isosceles right angled triangle, the perimeter
is 30 m. Find its area. (Approximate) ? ²

(a) 20 2 cm (b) 20  
2 + 1 cm
(a) 38.83 m² (b) 39.60 m²
(c) 37.86 m² (d) 40 m² (c) 10 cm (d) 10 + 
2 cm
6. The area of an isosceles right angled triangle is
121 cm². Find its hypotenuse.
²

4 FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA