**Chapter 10 Mensuration Ex 10.3**

Question 1.

Find the areas of the rectangles whose sides are:

(a) 3 cm and 4 cm

(b) 12 m and 21 m

(c) 2 km and 3 km

(d) 2 m and 70 cm

Solution:

(a) Length of the rectangle = 3 cm

Breadth of the rectangle = 4 cm

∴ Area of the rectangle = length x breadth = 3 cm x 4 cm

= 12 cm^{2} or 12 sq cm

(b) Length of the rectangle = 12 m and breadth = 21 m

∴ Area of the rectangle = length x breadth = 12 m x 21 m

= 252 m^{2} or 252 sq m

(c) Length of the rectangle = 2 km and breadth 3 km

∴ Area of the rectangle = length x breadth = 2 km x 3 km

= 6 km^{2} or 6 sq km

(d) Length of the rectangle = 2 m

and breadth = 70 cm or 0.70 m

∴ Area of the rectangle = length x breadth = 2 m x 0.70 m

= 1.40 m^{2} or 1.40 sq m

Question 2.

Find the areas of the squares whose sides are:

(a) 10 cm

(b) 14 cm

(c) 5 m

Solution:

(a) Side of the square = 10 cm

∴ Area of the square = Side x Side = 10 cm x 10 cm = 100 cm^{2} or 100 sq cm

(b) Side of the square = 14 cm

∴ Area of the square = Side x Side = 14 cm x 14 cm = 196 cm^{2} or 196 sq cm

(c) Side of the square = 5 m

∴ Area of the square = Side x Side = 5 m x 5 m = 25 m^{2} or 25 sq m

Question 3.

The length and breadth of three rectangles are as given below:

(a) 9 m and 6 m

(b) 17 m and 3 m

(c) 4 m and 14 m

Which one has the largest area and which one has the smallest?

Solution:

(a) Length of the rectangle = 9 m

and breadth = 6 m

∴ Area of the rectangle = length x breadth

= 9 m x 6 m

= 54 m^{2} or 54 sq m

(b) Length of the rectangle = 17 m

and breadth = 3m

∴ Area of the rectangle

= length x breadth = 17 m x 3 m 51 m^{2} or 51 sq m

(c) Length of the rectangle = 4 m

and breadth = 14 m

Area of the rectangle = length x breadth

= 4 m x 14 m

= 56 m^{2} or 56 sq m

Rectangle (c) has the largest area, i.e., 56 sq m and Rectangle (b) has the smallest area, i.e., 51 sq m.

Question 4.

The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.

Solution:

Length of the rectangular garden = 50 m

Area of the rectangular garden = 300 sq m

∴ Width = Area ÷ Length

= 300 sq m ÷ 50 m = 6 m

Hence width of the garden = 6 m.

Question 6.

A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?

Solution:

Length of the table-top = 2 m

and its breadth = 1 m 50 cm or 1.50 m

∴ Area of the table-top = length x breadth

= 2 m x 1.50 m

= 3 m^{2} or 3 sq m

Hence, the area of table-top = 3 sq m.

Question 7.

A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room?

Solution:

Length of the room = 4 m

and its breadth = 3 m 50 cm = 3.5 m

Area of the room = length x breadth

= 4 m x 3.5 m = 14 sq m

Hence, the area of the carpet needed = 14 sq m

Question 8.

A 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:

Length of the floor = 5 m

and its breadth = 4 m

∴ Area of the floor = length x breadth

= 5m x 4m = 20sqm

Side of the carpet = 3m

∴ Area of the square carpet = side x side = 3m x 3m = 9 sqm

∴ Area of the floor which is not carpeted = 20 sq m – 9 sq m

= 11 sq m.

Question 9.

Five square flower beds each of side 1 m are dug on a piece of land 5 m long and 4 m wide. What is the area of the remaining part of the land?

Solution:

Side of the square flower bed = 1 m.

∴ Area of 1 square flower bed = 1m x 1m = 1sqm.

∴ Area of 5 square flower beds = 1 sq m x 5 = 5 sq m.

Now length of the land = 5 m

and its breadth = 4 m

∴ Area of the land = length x breadth =5m x 4m = 20 sq m

∴ Area of the remaining part of the land = 20 sq m – 5 sq m

= 15 sq m.

Question 10.

By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).

Solution:

Splitting the given figure into the rectangles I, II, III and IV, we have

Area of the rectangle I = length x breadth

= 4 cm x 3 cm = 12 sq cm

Area of the rectangle II = length x breadth

= 3 cm x 2 cm = 6 sq cm.

Area of the rectangle III = length x breadth

= 4 cm x 1 cm = 4 sq cm

Area of the rectangle IV = length x breadth

= 3 cm x 2 cm = 6 sq cm

∴ Total area of the whole figure

= 12 sq cm + 6 sq cm + 4 sq cm + 6 sq cm

= 28 sq cm.

(b) Splitting the given figure into the rectangles I, II and III, we get

Area of the rectangle I

= 12 cm x 2 cm = 24 sq cm

Area of the rectangle II

= 8 cm x 2 cm = 16 sq cm

Area of rectangle III

= 3 cm x 1 cm = 3 sq cm

∴ Total area of the given figure = 3 sq cm + 3 sq cm + 3 sq cm = 9 sq cm.

Question 11.

Split the following shapes into rectangles and find their areas (The measures are given in centimetres).

Solution:

(a) Splitting the given figure into the rectangles I and II, we get

Area of the rectangle I

= 12 cm x 2 cm = 24 sq cm

Area of the rectangle II

= 8 cm x 2 cm = 16 sq cm

∴ Total area of the whole figure = 24 sq cm + 16 sq cm = 40 sq cm.

(b) Splitting the given figure into the rectangles I, II and III, we get

Area of the rectangle I

= 7 cm x 7 cm = 49 sq cm

Area of the rectangle II

= 21 cm x 7 cm = 147 sq cm

Area of the rectangle III

= 7 cm x 7 cm = 49 sq cm

∴ Total area of the whole figure

= 49 sq cm + 147 sq cm + 49 sq cm

= 245 sq cm.

Question 12.

How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to fit in a rectangular region whose length and breadth are respectively:

(a) 100 cm and 144 cm

(b) 70 cm and 36 cm

Solution:

Length of one tile = 12 cm

Breadth of the tile = 5 cm

∴ Area of 1 tile = length x breadth = 12 cm x 5 cm = 60 sq cm

(a) Length of the rectangular region = 144 cm

Breadth of the region = 100 cm

∴ Area of the rectangular region = length x breadth = 144 cm x 100 cm

= 14400 sq cm

∴ Number of tiles needed to cover the whole rectangular region

= 14400 sq cm ÷ 60 sq cm

= 240 tiles

(b) Length of the rectangular region = 70 cm

Breadth of the region = 36 cm

∴ Area of the rectangular region = length x breadth = 70 cm x 36 cm = 2520 sq cm

∴ Number of tiles needed to cover the whole rectangular region

= 2520 sq cm ÷ 60 sq cm

= 42 tiles.