# Mensuration

## Exercise 10.3

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) 3 cm and 4 cm

Given: length = 3 cm

breadth = 4 cm

Area of rectangle = length X breadth

= 3 X 4

= 12 cm^{2}

(b) 12 m and 21 m

Given: length = 12 m

breadth = 21 m

Area of rectangle = length X breadth

= 12 X 21

= 252 m^{2}

(c) 2 km and 3 km

Given: length = 2 km

breadth = 3 km

Area of rectangle = length X breadth

= 2 X 3

= 6 km^{2}

(d) 2 m and 70 cm

Given: length = 2 m

breadth = 70 cm = 0.70 m

Area of rectangle = length X breadth

= 2 X 0.70

= 1.40 m^{2}

2). Find the areas of the squares whose sides are:

(a) 10 cm (b) 14 cm (c) 5 m

Solution:

(a) 10 cm

Given: side = 10 cm

Area of square = side X side

= 10 X 10

= 100 cm^{2}

(b) 14 cm

Given: side = 14 cm

Area of square = side X side

= 14 X 14

= 196 cm^{2}

(c) 5 m

Given: side = 5 m

Area of square = side X side

= 5^{2}

= 5 X 5

= 25 m^{2}

3). The length and breadth of the 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) 9 m and 6 m

Given: length = 9 m

breadth = 6 m

Area of rectangle = length X breadth

= 9 X 9

= 54 m^{2}

(b) 17 m and 3 m

Given: length = 17 m

breadth = 3 m

Area of rectangle = length X breadth

= 17 X 3

= 51 m^{2}

(c) 4 m and 14 m

Given: length = 4 m

breadth = 14 m

Area of rectangle = length X breadth

= 4 X 14

=56 m^{2}

Ans: rectangle b has the smallest area and rectangle c has the largest area.

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

Given: length of the rectangular garden = 50 m

Area of the rectangular garden = 300 sq m

To find: Breadth of the garden = ?

Area of garden = length X breadth

300 = 50 X breadth

50 X breadth = 300

Breadth = 300 ÷ 50

=6 m

Ans: breadth of the garden = 6 m

5). What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹ 8 per hundred sq m.?

Given: length of the rectangular plot = 500 m

breadth of the plot = 200 m

rate of tilling the plot = ₹ 8 per hundred sq m

to find: Cost of the tilling the plot = ?

Area of plot = length X breadth

= 500 X 200

= 100000 m^{2}

Cost of tilling = Rate X Area

= (8/ 100) X 100000

= (8 X 100000) ÷ 100

= 800000 ÷ 100

= 8000

Ans: cost of tilling the plot = ₹ 8000

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

Given: length of the table top= 2 m

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

Area of table top = length X breadth

= 2 X 1.50

=3.00 m^{2}

Ans: area of the table-top = 3 m^{2}

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?

Given: length of the room = 4 m

breadth of the room = 3 m 50 cm = 3.50 m

Area of room = length X breadth

= 4 X 3.50

=14.00 m^{2}

Ans: carpet needed to cover the floor = 14 m^{2}

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.

Given: length of the floor = 5 m

Breadth of the floor = 4 m

Side of the square carpet = 3 m

Area of the floor = length X breadth

= 5 X 4

=20 m^{2}

Area of the carpet = side^{2}

= 3^{2}

= 9 m^{2}

Area of the floor not carpeted = Area of the floor – area of the carpet

= 20 – 9

= 11

Ans: Area of the floor not carpeted = 9 m^{2}

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?

Given: length of the land = 5 m

Breadth of the land = 4 m

Side of the square flower blade = 1 m

Area of the floor = length X breadth

= 5 X 4

=20 m^{2}

Area of square = side X side

= 1 m^{2}

Area of the 5 flower beds = 5 X 1

= 5 m^{2}

Area of the remaining part of the land = Area of the land

– area of 5 flower beds

= 20 – 5

= 15

Ans: Area of the remaining part of the land = 15 m^{2}

10). By splitting the following figures into rectangles, find their areas

(The measures are given in centimetres).

For Rectangle 1

Given: length = 2 cm

breadth = 1 cm

Area of rectangle = length X breadth

= 2 X 1

= 2 cm^{2}

For rectangle 2

Given: length = 5 cm

breadth = 1 cm

Area of rectangle = length X breadth

= 5 X 1

= 5 cm^{2}

For rectangle 3

Given: length = 2 cm

breadth = 1 cm

Area of rectangle = length X breadth

= 2 X 1

= 2 cm^{2}

Area of the figure = 5 + 2 + 2

= 9 cm^{2}

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

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:

(a) 100 cm and 144 cm

Length = 100 cm

Breadth = 144 cm

Area of rectangle = length X breadth

= 100 X 144

= 14400 cm^{2}

Length of the tile = 12 cm

breadth of the tile = 5 cm

Area of the tile = length X breadth

= 12 X 5

= 60 cm^{2}

Number of tiles = __area of the region__

area of the tile

= 14400/60

= 240

(b) 70 cm and 36 cm.

Length = 70 cm

Breadth = 36 cm

Area of rectangle = length X breadth

= 70 X 36

= 2520 cm^{2}

Length of the tile = 12 cm

breadth of the tile = 5 cm

Area of the tile = length X breadth

= 12 X 5

= 60 cm^{2}

Number of tiles = __area of the region__

area of the tile

= 2520/60

=42

Click here for the solutions of

Chapter 10 Mensuration

Chapter 8 Decimals

Chapter 7 Fractions

Chapter 6 Integers

Chapter 5 Understanding Elementary Shapes

Chapter 4 Basic Geometrical Ideas

Chapter 3: Playing With Numbers

Chapter 2: Whole Numbers

Chapter 1: Knowing Our Numbers