**Chapter 10 Mensuration**

### Very Short Answer Type

Question 1.

The perimeter of a square is 64 cm. Find the length of each side.

Solution:

Perimeter of the square = 64 cm

Question 2.

Length and breadth of a rectangular table-top are 36 cm and 24 cm respectively. Find its perimeter.

Solution:

Length of the rectangular table-top = 36 cm

and its breadth = 24 cm.

∴ Perimeter of the table-top = 2 [length + breadth]

= 2 [36 cm + 24 cm]

= 2 x 60 cm = 120 cm.

Question 3.

Which of the following figure has greater perimeter?

Solution:

Fig. (i) Perimeter of the square = 4 x side

= 4 x 4 cm = 16 cm

Fig. (ii) Perimeter of the rectangle

= 2 [length + breadth]

= 2[8 cm + 3 cm]

= 2 x 11 cm = 22 cm

Since 22 cm > 16 cm

∴ Rectangle has greater perimeter than the square.

Question 4.

How much distance will you have to travel in going around each of the following figures?

Solution:

Distance travelled in going around Fig. (i)

= 12 cm + 3 cm + 12 cm + 3 cm = 30 cm

Distance travelled in going around Fig. (ii)

= 6 cm + 4 cm + 4 cm + 4 cm = 18 cm

Question 5.

Find the perimeter of a square whose side is 15 cm.

Solution:

Side of the square = 15 cm

∴ Perimeter of the square = 15 cm x 4 = 60 cm

Question 6.

Find the cost of fencing a rectangular park 300 m long and 200 m wide at the rate of ₹4 per metre.

Solution:

Length of the park = 300 m

Breadth = 200 m

∴ Perimeter of the park = 2 [length + breadth]

= 2 [300 m + 200 m]

= 2 x 500 m = 1000 m.

Cost of fencing the rectangular park = 1000 x 4 = ₹4000

Question 7.

Find the area of a square field whose each side is 150 m.

Solution:

Side of the square field = 150 m

∴ Area of the square field = Side x Side

= 150 m x 150 m

= 22500 sq m.

Question 8.

Length and breadth of a rectangular paper are 22 cm and 10 cm respectively. Find the area of the paper.

Solution:

Length of the rectangular paper = 22 cm

Breadth = 10 cm

∴ Area of the rectangular paper = length x breadth

= 22 cm x 10 cm

= 220 sq cm.

### Short Answer Type

Question 9.

Find the length of a rectangle given that its perimeter is 880 m and breadth is 88 m.

Solution:

Perimeter of the rectangle = 2 [length + breadth]

∴ 2 [length + breadth] = 880

length + breadth = 880 ÷ 2 = 440

∵ Breadth = 88 m

∴ Length = 440 m – 88 m = 352 m

Hence, the required length = 352 m.

Question 10.

How many trees can be planted at a distance of 6 metres each around a rectangular plot whose length is 120 m and breadth is 90 m?

Solution:

Length of the rectangular plot = 120 m

Breadth = 90 m

∴ Perimeter of the rectangular plot

= 2 [length + breadth]

= 2 [120 m + 90 m]

= 2 x 210 m = 420 m

Now distance between two trees = 6 m

∴ Number of trees around the rectangular plot = 420 m ÷ 6 m = 70

Question 11.

A rectangular park is 30 metres long and 20 metres broad. A steel wire fence is put up all around it. Find the cost of putting the fence at the rate of ₹15 per metre.

Solution:

Length of the rectangular park = 30 m

Breadth = 20 m

∴ Perimeter of the rectangular park = 2(length + breadth)

= 2 [30 + 20] = 2 x 50 m = 100 m

∴ Cost of fencing all around the park = ₹15 x 100 = ₹1500

Question 12.

Find the area of the figures A, B, C and D drawn on a squared paper in the following figure by counting squares.

Solution:

(A) Counting the squares, we have 8 squares

∴ Area = 8 sq units

(B) Counting the squares, we have 4 squares

∴ Area = 4 sq units

(C) Counting the squares, we have 5 squares

∴ Area = 5 sq units

(D) Counting the squares, we have 7 squares

∴ Area = 7 sq units

### Higher Order Thinking Skills (HOTS)

Question 13.

A rectangle and a square have the same perimeter 100 cm. Find the side of the square. If the rectangle has a breadth 2 cm less than that of the square. Find the breadth, length and area of the rectangle.

Solution:

Perimeter of the square = 100 cm

Perimeter 100

= 25 cm.

∴ Breadth of the rectangle = 25 cm – 2 cm = 23 cm

Now perimeter of the rectangle = 100 cm

∴ 2 [length + breadth] = 100

length + breadth = 100 ÷ 2 = 50 cm

But breadth = 23 cm

∴ Length = 50 cm – 23 cm = 27 cm

Now, Area of the rectangle

= length x breadth = 27 cm x 23 cm

= 621 sq cm.

Question 14.

Fencing the compound of a house costs ₹5452. If the rate is ₹94 per metre, find the perimeter of the compound. If the breadth is 10 m, find its length.

Solution:

Cost of fencing the compound = ₹5452

and the rate of fencing = ₹94 per metre

∴ Perimeter of the compound = 5452 ÷ 94 = 58 metres

Now breadth of the compound = 10 m.

2 [length + breadth] = 58 m

∴ length + breadth = 58 + 2 m = 29 m

∴ Length of the compound = 29 m – 10 m = 19 m.