Mensuration Class 8 questions and solutions are provided here to help students score good marks in the examination. All these questions given here are based on the latest NCERT syllabus of Class 8 maths. Students can start solving the questions given below to improve their skills in mensuration.

What is Mensuration?

Mensuration is one of the branches of mathematics that deals with measuring various geometric shapes, such as a triangle, square, rectangle, cube, cuboid, cone, sphere, etc.

Mensuration Formulas

Some of the important formulas of mensuration are given below:

  • Perimeter of a triangle = Sum of sides
  • Perimeter of a square = 4 × side
  • Area of a square = side × side
  • Perimeter of a rectangle = 2(Length + Breadth)
  • Area of a rectangle = Length × Breadth
  • Perimeter of a regular polygon with n sides = n × side
Also read:

Mensuration Class 8 Questions and Answers

1. Find the perimeter of a rectangle whose length and breadth are 250 cm and 1 m, respectively.

Solution:

Given,

Length of a rectangle = 250 cm

Breadth of a rectangle = 1 m = 100 cm

Perimeter of a rectangle = 2(Length + Breadth)

= 2(250 + 100)

= 2 × 350

= 700 cm

Therefore, the perimeter of a rectangle is 700 cm.

2. What is the perimeter and area of the square with a side of 7 cm?

Solution:

Given,

Side of a square = 7 cm

Perimeter of a square = 4 × side

= 4 × 7

= 28 cm

Area of a square = (side)2

= 72

= 49 cm2

Hence, the perimeter of a square is 28 cm, and the area of the square is 49 cm2.

3. Calculate the area of the rectangle with a length of 80 units and a breadth of 45 units.

Solution:

Given,

Length of a rectangle = 80 units

Breadth of a rectangle = 45 units

Area of a rectangle = Length × Breadth

= 80 × 45

= 3600

Thus, the area of a rectangle is 3600 square units.

4. What is the perimeter of an equilateral triangle with sides 13 cm?

Solution:

Given,

Side of an equivalent triangle = 13 cm

Perimeter of equivalent triangle = 3 × side

= 3 × 13

= 39

Therefore, the perimeter of an equivalent triangle is 39 cm.

5. Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.

Solution:

Given.

Sides of a triangle are:

a = 10 cm

b = 14 cm

c = 15 cm

Perimeter of a triangle = a + b + c

= (10 + 14 + 15) cm

= 39 cm

Therefore, the perimeter of the triangle is 39 cm.

6. An athlete takes 5 rounds of a rectangular park of 100 m long and 50 m wide. Calculate the total distance covered by him.

Solution:

Given,

Length of the rectangular park = 100 m

Breadth of the rectangular park = 50 m

Total distance covered by the athlete in one round = Perimeter of the rectangular

= 2 × (length + breadth)

= 2 × (100 + 50)

= 2 × 150

= 300 m

Thus, the distance covered in 5 rounds = 5 × 300 m = 1500 m

7. Find the cost of fencing a rectangular park of 225 m in length and breadth of 200 m at Rs. 12 per meter.

Solution:

Given,

Length of the rectangular park = 225 m

Breadth of the rectangular park = 200 m

Perimeter of the rectangle = 2 × (length + breadth)

= 2 × (225 m + 200 m)

= 2 × (425 m)

= 850 m

Thus, the perimeter of the rectangular park is 850 m.

Cost of fencing 1 m of park = Rs. 12

So, the total cost of fencing the park = Rs. 12 × 850 = Rs. 10200

8. If the perimeter of a regular hexagon is 42 cm, find the length of each side.

Solution:

As we know, a regular hexagon has 6 sides of equal length.

Let s be the side length of a regular hexagon.

Given that the perimeter of a regular hexagon = 42 cm

6s = 42

s = 42/6 = 7

Therefore, the length of each side of a regular hexagon is 7 cm.

9. A piece of string is 30 cm long. What will be the length of each side of the string is used to form:

(a) A square?

(b) An equilateral triangle?

(c) A regular pentagon?

Solution:

Given,

Length of a string = 30 cm

(a) String is in the form of a square

Perimeter of square = 30 cm

4 × side = 30

Side = 30 / 4 = 7.5 cm

Side of the square = 7.5 cm

(b) String is in the form of an equilateral triangle

Perimeter of an equilateral triangle = 30 cm

3 × side = 30

Side = 30 / 3 = 10 cm

Side of an equilateral triangle = 10 cm

(c) String is in the form of a regular pentagon

Perimeter of a regular pentagon = 30 cm

5 × side = 30

Side = 30 / 5 = 6 cm

Side of a regular pentagon = 5 cm

10. The floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.

Solution:

Given,

  • A floor with 4 m wide and 5 m length
  • A square carpet of side 3 m

Area of the floor = length × breath

= 5 × 4

= 20 m2

Area of the square carpet = side × side

= 3 × 3

= 9 m2

Hence, the area of the floor that is not carpeted = Area of the floor – Area of the square carpet

= 20 – 9

= 11 m2

Therefore, the floor area that is not carpeted is 11 m2.

Practice Questions on Mensuration Class 8

  1. A table-top measures 4 m by 2 m 50 cm. What is its area in square meters?
  2. The area of a rectangular piece of cardboard is 36 sq cm, and its length is 9 cm. What is the width of the cardboard?
  3. Find the area of a square plot of side 18 m.
  4. What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide, at the rate of Rs. 8 per hundred sq m.?
  5. Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?