CBSE Class 6th Solutions, Class 6th Maths Solutions
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Questions and Solutions for NCERT Class 6 Mathematics Chapter 10 – Mensuration – Exercise 10.1

Questions and Solutions for NCERT Class 6 Mathematics Chapter 10 – Mensuration – Exercise 10.1

1. Find the perimeter of each of the following figures :

Solution: 

(a) Perimeter = Sum of all the sides of the figure

= 4 cm + 2 cm + 1 cm + 5 cm

= 12 cm

(b) Perimeter = Sum of all the sides of the figure

= 23 cm + 35 cm + 40 cm + 35 cm

= 133 cm

(c) Perimeter = Sum of all the sides of the figure 

= 15 cm + 15 cm + 15 cm + 15 cm

= 60 cm

(d) Perimeter = Sum of all the sides of the figure

= 4 cm + 4 cm + 4 cm + 4 cm + 4 cm

= 20 cm

(e) Perimeter = Sum of all the sides of the figure

= 1 cm + 4 cm + 0.5 cm + 2.5 cm + 2.5 cm + 0.5 cm + 4 cm

= 15 cm

(f) Perimeter = Sum of all the sides of the figure

= 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm +3 cm

= 52 cm

2. The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?

Solution: Total length of the tape required = Perimeter of the rectangular box

= 2 * ( Length + Breadth)

= 2 * ( 40 + 10 )

= 2 * 50

= 100 cm

Therefore, length of the tape required = 100 cm

3. A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?

Solution: Perimeter of the table top = Perimeter of the rectangle

= 2* ( Length + Breadth )

Length of the table top = 2 m 25 cm = 2.25 m

Breadth of the table top = 1 m 50 cm = 1.50 m

Perimeter = 2 * ( 2.25 + 1.50 )

= 2 * 3.75

= 7.50 m or 750 cm

Therefore perimeter of the table top = 7.5 m

4. What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?

Solution: The length of the wooden strip required to frame a photograph = Perimeter of the photograph 

Perimeter = 2 * ( Length + Breadth )

= 2 * ( 32 + 21 )

= 2 * 53

= 106 cm

Therefore, length of the wooden strip required to frame a photograph = 106 cm

5. A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?

Solution: Since each side is to be fenced with 4 rows of wires

Length of the wire required = 4 * Perimeter of the rectangular land

Perimeter of the Land = 2 * ( L + B )

= 2 * ( 0.7 + 0.5 )

= 2 * 1.2

= 2.4 km

Length of the wire required = 4 * 2.4 = 9.6 km

6. Find the perimeter of each of the following shapes :
(a) A triangle of sides 3 cm, 4 cm and 5 cm.

Solution: Perimeter of ΔABC = AB + BC + AC

= 3 + 4 + 5

= 12 cm

(b) An equilateral triangle of side 9 cm.

Solution: Perimeter of an equilateral triangle = 3 * side

= 3 * 9 

= 27 cm

(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.

Solution: Perimeter of ΔABC = AB + BC + AC

= 8 + 6 + 8

= 22 cm

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

Solution: Perimeter of triangle = Sum of all three sides

= 10 + 14 + 15

= 39 cm

8. Find the perimeter of a regular hexagon with each side measuring 8 m.

Solution: Perimeter of a regular hexagon = 6 * side

= 6 * 8

= 48 m

Therefore, perimeter of Hexagon is 48 m

9. Find the side of the square whose perimeter is 20 m.

Solution: Perimeter of a square = 4 * side

Therefore, Side = Perimeter/4

Perimeter = 20 m

Side = 20/4

= 5 cm

Thus, the side of the square = 5 cm

10. The perimeter of a regular pentagon is 100 cm. How long is its each side?

Solution: Perimeter of a regular pentagon = 5 * side

Therefore, Side = Perimeter/5

Perimeter = 100 cm

Side = 100/5

= 20 cm

Thus, the side of the regular pentagon = 20 cm

11. A piece of string is 30 cm long. What will be the length of each side if the string is used to form :
(a) a square?

Solution: Length of the string = Perimeter of square

Perimeter of a square = 4 * side

Therefore, Side = Perimeter/4

Perimeter = 30 m

Side = 30/4

= 7.5 cm

Thus, the side of the square = 7.5 cm

(b) an equilateral triangle?

Solution: Length of the string = Perimeter of the equilateral triangle

Perimeter of equilateral triangle = 3 * Side

Side = Perimeter/3

Given, Perimeter = 30

Side = 30/3

= 10 cm

Therefore, Side of the Equilateral triangle = 10 cm

(c) a regular hexagon?

Solution: Length of the string = Perimeter of the equilateral triangle

Perimeter of regular hexagon = 6 * Side

Side = Perimeter/6

Given, Perimeter = 30

Side = 30/6

= 5 cm

Therefore, Side of the Regular Hexagon = 5 cm

12. Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?

Solution: Perimeter of a triangle = Sum of all the sides

Let, the third side be x

Then, 12 + 14 + x = 36

26 + x = 36 

x = 36 – 26

x = 10 

Therefore, third side of the triangle = 10 cm

13. Find the cost of fencing a square park of side 250 m at the rate of Rs 20 per metre.

Solution: Side of the square = 250 m

Perimeter of the square = 4 * side

= 4 * 250

= 1000 m

Cost of fencing per metre = Rs. 20

Therefore, cost of fencing square park = 1000 * 20

= Rs. 20,000

14. Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of Rs 12 per metre.

Solution: Length of the rectangular park = 175 m

Breadth of the rectangular park = 125 m 

Perimeter of the park = 2 * ( L + B )

= 2 * ( 175 + 125 )

= 2 * 300

= 600 m

Rate of fencing per metre = Rs. 12

Therefore, cost of fencing the rectangular park = 12 * 600

= Rs. 7,200

15. Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance?

Solution: Perimeter of the square park = 4 * Side

= 4 * 75

= 300 m

Thus, distance covered by Sweety is 300 m

Perimeter of the rectangular park = 2 *( L + B )

= 2 * ( 60 + 45 )

= 2 * 105

= 210 m

Thus, distance covered by Bulbul is 210 m

So, Bulbul covers less distance than Sweety.

16. What is the perimeter of each of the following figures? What do you infer from the answers?

Solution:

(a) Perimeter of square = 4 * Side

= 4 * 25

= 100 cm

(b) Perimeter of a rectangle = 2 * ( L + B )

= 2 * ( 20 + 30 )

= 2 * 50

= 100 cm

(c) Perimeter of a rectangle = 2 * ( L + B )

= 2 * ( 10 + 40 )

= 2 * 50

= 100 cm

(d) Perimeter of triangle = Sum of all the sides = 30 + 30 + 40

= 100 cm 

Thus, all figures have same perimeter.

17. Avneet buys 9 square paving slabs, each with a side of 1/2 m. He lays them in the form of a square.

(a) What is the perimeter of his arrangement 

Answer: 6 m

(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement?

Answer: 10 m

(c) Which has greater perimeter?

Answer: Second arrangement has greater perimeter.

(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)

Answer: If all the slabs are arranged in a row, the perimeter will be 10 m.

You can find the solutions for Class 6 Mathematics previous exercises from here

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