# Mensuration Questions For NMAT:

Download Mensuration Questions for NMAT PDF. Top 10 very important Mensuration Questions for NMAT based on asked questions in previous exam papers.

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**Question 1: **If the diagonal of a square is 10 metres, find its area?

a) 10

b) 20

c) 30

d) 40

e) None of the above

**Question 2: **If the radius of a circle is equal to the side of a square, what is the ratio of the perimeters of the circle to the square?

a) $\pi$:1

b) $\pi$:2

c) $\pi$:3

d) 2:$\pi$

e) None of the above

**Question 3: **The circumference of a circle is 100 $\pi$ metres. Find its area?

a) 2500 $\pi$

b) 3000 $\pi$

c) 3500 $\pi$

d) 3600 $\pi$

e) None of the above

**Question 4: **The length of a rectangle is 24 metres and its perimeter is 84 metres. Find the area of a triangle whose base is equal to the breadth of the rectangle and height equal to the rectangle’s diagonal?

a) 200

b) 210

c) 240

d) 270

e) None of the above

**Question 5: **The length of a rectangle is twice its breadth. If the area of the rectangle is 50 metre square, what is the length of the rectangle?

a) 5 metres

b) 10 metres

c) 25 metres

d) 50 metres

e) None of the above

**Instructions**

Instructions: Study the following diagram to answer the questions.

**Question 6: **If it is known that the the radius of each of the inscribed circles is 7 units then the area of the shaded region of square ABCD is ?

a) 186 sq. cm

b) 168 sq. cm

c) 188 sq. cm

d) 198 sq. cm

**Question 7: **If the diameter of a circle is equal to the diagonal of a square of area 100 sq. cms, what is the area of the circle?

a) 25 $\pi$

b) 50 $\pi$

c) 75 $\pi$

d) 100 $\pi$

e) None of the above

**Question 8: **The length of a rectangle is thrice it’s breadth. The perimeter of the rectangle is 544 metres.

What is it’s area?

a) 18372

b) 23872

c) 13872

d) Can’t be determined

e) None of the above

**Question 9: **The length of a rectangle is thrice it’s breadth. The perimeter of the rectangle is 544 metres.

What is it’s area?

a) 18372

b) 23872

c) 13872

d) Can’t be determined

e) None of the above

**Question 10: **A rectangular football ground has grass around it of length 2 metres on each side. The perimeter of the field is 200 metres. How much does it cost to have the grass cut at the rate of Rs 100 per sq metre?

a) 4000

b) 2000

c) 1000

d) Can’t be determined

e) None of the above

**Question 11: **In a right angled traingle, two of the sides are of equal length. Which of the following is certainly one of the angles in the triangle?

a) 30

b) 45

c) 60

d) 75

e) Can’t be determined

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**Answers & Solutions:**

**1) Answer (E)**

Diagonal = $ \sqrt {2} $times the side. So, the area = $ \frac {(diagonal) ^ {2}}{2} $= 50 square metres.

**2) Answer (B)**

The required ratio is 2*$\pi$*r : 4*r = $\pi$:2

**3) Answer (A)**

Circumference = 2*$\pi$*r = 100 $\pi$. So, r = 50 metres. Area = $\pi$* r * r = 2500 $\pi$

**4) Answer (D)**

If the perimeter of the rectangle is 84, 2 * (l + b) = 84. So, breadth is 18 metres since length is 24. $ diagonal^{2} = length^{2} + breadth^{2}$. So, diagonal = 30. Area of the triangle = ½*base*height = ½* 18*30 = 270

**5) Answer (B)**

If the breadth is s, length is 2s and area = 2s * s = 50. So, s is 5 and 2s is 10.

**6) Answer (B)**

Area of square = 28 x 28 = 784 sq.cm

Area of four circles = 4$\pi$r^{2}

= 4 x $\frac{22}{7}$ x 7 x 7 = 616 sq.cm

Area of shaded region

= 784 – 616 = 168 sq. cm

**7) Answer (B)**

length of diagonal = $\sqrt{100}$*$\sqrt{2}$ = diameter. Radius = diameter/2. Area = $\pi$*$radius^{2}$

**8) Answer (C)**

If the breadth is x, length = 3x. Perimeter = 2*(x+3x) = 544. so, breadth = 68 and length = 204. Area = 68*204

**9) Answer (C)**

If the breadth is x, length = 3x. Perimeter = 2*(x+3x) = 544. so, breadth = 68 and length = 204. Area = 68*204

**10) Answer (D)**

Perimeter of 200 metres is possible for infinite rectangles. Just the length of grass is not sufficient to determine the area of the grass.

**11) Answer (B)**

This is a symmetric right angled traingle. So, the angles will be 45, 45 and 90.

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