## MP Board Class 6th Maths Solutions 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 21m

(c) 2 km and 3 km

(d) 2 m and 70 cm

Solution:

(a) Area of rectangle = length × breadth

= 3 cm × 4 cm = 12 cm^{2}

(b) Area of rectangle = length × breadth

= 12 m × 21 m = 252 m^{2}

(c) Area of rectangle = length × breadth

= 2 km × 3 km = 6 km^{2}

(d) Area of rectangle = length × breadth

= 2 m × 70 cm = 2 m × 0.7 m = 1.4 m^{2}

Question 2.

Find the areas of the squares whose sides are:

(a) 10 cm

(b) 14 cm

(c) 5 m

Solution:

(a) Area of square = side × side

= 10 cm × 10 cm = 100 cm^{2}

(b) Area of square = side × side

= 14 cm × 14 cm = 196 cm^{2}

(c) Area of square = side × side

= 5 m × 5 m = 25 m^{2}

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) Area of rectangle = length × breadth

= 9m × 6m = 54m^{2}

(b) Area of rectangle = length × breadth

= 17 m × 3 m = 51 m^{2}

(c) Area of rectangle = length × breadth

= 4 m × 14 m = 56 m^{2}

Thus, rectangle (c) has the largest area, i.e. 56 m^{2} and rectangle (b) has the smallest area, i.e., 51 m^{2}.

Question 4.

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

SolutionL

Length of rectangle = 50 m

Area of rectangle = 300 m^{2}

Since, area of rectangle = length × breadth

Therefore, breadth = \(\frac{\text { area of rectangle }}{\text { length }}\)

= \(\frac{300}{50}\) m = 6 m

Thus, the breadth of the garden is 6 m.

Question 5.

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?

Solution:

Length of land = 500 m

Breadth of land = 200 m

Area of land = length × breadth

= 500 m × 200 m = 1,00,000 sq m

Cost of tiling 100 sq m of land = Rs. 8

∴ Cost of tiling 1,00,000 sq m of land

= Rs. \(\frac{8 \times 100000}{100}\) = Rs. 8000

Question 6.

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

Solution:

Length of table-top = 2 m

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

∴ Area of table-top = length × breadth

= 2 m × 1.50 m = 3 m^{2}

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 room = 4 m

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

∴ Area of carpet = length × breadth

= 4 m × 3.50 m = 14 m^{2}

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 floor = 5 m

And breadth of floor = 4 m

Area of floor = length × breadth

= 5m × 4m = 20m^{2}

Now, side of square carpet = 3 m

Area of square carpet = side × side

= 3m × 3m = 9m^{2}

∴ Area of floor that is not carpeted

= 20 m^{2} – 9 m^{2} = 11 m^{2}

Question 9.

Five square flower beds each of sides 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 square flower bed = 1 m Area of square flower bed = side × side

= 1m × 1m = 1m^{2}

∴ Area of 5 square flower beds = (1 × 5) m^{2}

= 5 m^{2}

Now, length of land = 5 m

And breadth of land = 4 m

∴ Area of land = length × breadth = 5m × 4m

= 20 m^{2}

∴ Area of remaining part

= Area of land – Area of 5 flower beds

= 20 m^{2} – 5 m^{2} = 15 m^{2}

Question 10.

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

Solution:

(a) We have,

Area of square HKLM = 3 × 3 cm^{2} = 9 cm^{2}

Area of rectangle I]CH = 1 × 2 cm^{2} = 2 cm^{2}

Area of square FEDG = 3 × 3 cm^{2} = 9 cm^{2}

Area of rectangle ABCD = 2 × 4 cm^{2} = 8 cm^{2}

∴ Total area of the figure = (9 + 2 + 9 + 8) cm^{2} = 28 cm^{2}

(b) We have,

Area of rectangle ABCD = 3 × 1 cm^{2} = 3 cm^{2}

Area of rectangle BJEF = 3 × 1 cm^{2} = 3 cm^{2}

Area of rectangle FGHI = 3 × 1 cm^{2} = 3 cm^{2}

∴ Total area of the figure = (3 + 3 + 3) cm^{2} = 9 cm^{2}

Question 11.

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

Solution:

(a) We have,

Area of rectangle ABCD = 2 × 10 cm^{2} = 20 cm^{2}

Area of rectangle DEFG = 10 × 2 cm^{2} = 20 cm^{2}

∴ Total area of the figure = (20 + 20) cm^{2}

= 40 cm^{2}

(b) We have,

There are 5 squares each of side 7 cm.

Area of one square = 7 × 7 cm^{2} = 49 cm^{2}

∴ Area of 5 squares = 5 × 49 cm^{2} = 245 cm^{2}

(c) We have,

Area of rectangle ABCD = 5 × 1 cm^{2} = 5 cm^{2}

Area of rectangle EFGH = 4 × 1 cm^{2} = 4 cm^{2}

∴ Total area of the figure = (5 + 4) cm^{2}

= 9 cm^{2}

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:

(a) Area of rectangular region

= length × breadth = 100 cm × 144 cm = 14400 cm^{2}

Area of one tile = 12 cm × 5 cm = 60 cm^{2}

Thus, 240 tiles are required.

(b) Area of rectangular region

= length × breadth = 70 cm × 36 cm = 2520 cm^{2}

Area of one tile = 12 cm × 5 cm = 60 cm^{2}

∴ Number of tiles

= \(\frac{\text { Area of rectangular region }}{\text { Area of one tile }}=\frac{2520}{60}\) = 40

Thus, 42 tiles are required.