NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.3

NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.3 are the part of NCERT Solutions for Class 6 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.3.

NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.3 (Rationalised Contents)

Ex 10.3 Class 6 Maths 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) Given: Length of the rectangle = 3 cm
Breadth of the rectangle = 4 cm
∴ Area of the rectangle = length × breadth = 3 cm × 4 cm
= 12 cm²

(b) Given: Length of the rectangle = 12 m

Breadth of the rectangle = 21 m
∴ Area of the rectangle = length × breadth = 12 m × 21 m
= 252 m²

Breadth of the rectangle = 3 km
∴ Area of the rectangle = length × breadth = 2 km × 3 km
= 6 km²

(d) Given: Length of the rectangle = 2 m
Breadth of the rectangle = 70 cm = 70/100 m = 0.7 m
∴ Area of the rectangle = length × breadth = 2 m × 0.7 m
= 1.4 m²

Ex 10.3 Class 6 Maths Question 2.

Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 m

Solution:
(a) Given: Side of the square = 10 cm
∴ Area of the square = Side × Side = 10 cm × 10 cm = 100 cm²
(b) Given: Side of the square = 14 cm
∴ Area of the square = Side × Side = 14 cm × 14 cm = 196 cm²
(c) Given: Side of the square = 5 m
∴ Area of the square = Side × Side = 5 m × 5 m = 25 m²

Ex 10.3 Class 6 Maths 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) Given: Length of the rectangle = 9 m
Breadth of the rectangle = 6 m
∴ Area of the rectangle = length × breadth
= 9 m × 6 m
= 54 m²

(b) Given: Length of the rectangle = 17 m
Breadth of the rectangle = 3 m
∴ Area of the rectangle
= length × breadth = 17 m × 3 m = 51 m²

(c) Given: Length of the rectangle = 4 m
Breadth of the rectangle = 14 m
∴ Area of the rectangle = length × breadth
= 4 m × 14 m
= 56 m²
Rectangle given in (c) has the largest area, i.e., 56 sq. m and the Rectangle given in (b) has the smallest area, i.e., 51 sq. m.

Ex 10.3 Class 6 Maths Question 4.

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

Solution:
Given: Length of the rectangular garden = 50 m
Area of the rectangular garden = 300 sq. m
∴ Width of the garden = Area ÷ Length
= 300 sq. m ÷ 50 m = 6 m
Hence, width of the garden is 6 m.

Ex 10.3 Class 6 Maths Question 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?

Solution:
Given: Length of the rectangular plot = 500 m
Breadth of the rectangular plot = 200 m
∴ Area of the plot = length × breadth = 500 m × 200 m = 1,00,000 sq. m
Now, rate of tiling the plot = ₹ 8 per 100 sq. m
Cost of tiling the garden = ₹ (8/100 × 1,00,000) = ₹ 8000
Hence, the required cost is ₹ 8000.

Ex 10.3 Class 6 Maths Question 6.

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

Solution:
Given: Length of the table-top = 2 m
Breadth of the table-top = 1 m 50 cm = 1.5 m
∴ Area of the table-top = length × breadth
= 2 m × 1.5 m
= 3 m²
Hence, the area of table-top is 3 sq. m.

Ex 10.3 Class 6 Maths 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:
Given: Length of the room = 4 m
Breadth of the room = 3 m 50 cm = 3.5 m
Area of the room = length × breadth
= 4 m × 3.5 m = 14 sq. m
Hence, the area of the carpet needed to cover the floor is 14 sq. m.

Ex 10.3 Class 6 Maths 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:
Given: Length of the floor = 5 m
Breadth of the floor = 4 m
∴ Area of the floor = length × breadth
= 5 m × 4 m = 20 sq. m
Side of the carpet = 3 m
∴ Area of the square carpet = side × side = 3 m × 3 m = 9 sq. m
∴ Area of the floor which is not carpeted = 20 sq. m – 9 sq. m
= 11 sq. m

Ex 10.3 Class 6 Maths 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:
Given: Side of the square flower bed = 1 m
∴ Area of 1 square flower bed = 1 m × 1 m = 1 sq. m
∴ Area of 5 square flower beds = 1 sq. m × 5 = 5 sq. m
Now, length of the land = 5 m
Breadth of the land = 4 m
∴ Area of the land = length × breadth = 5 m × 4 m = 20 sq. m
∴ Area of the remaining part of the land = 20 sq. m – 5 sq. m
= 15 sq. m

Ex 10.3 Class 6 Maths 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 × breadth
= 4 cm × 3 cm = 12 sq. cm
Area of the rectangle II = length × breadth
= 3 cm × 2 cm = 6 sq. cm
Area of the rectangle III = length × breadth
= 4 cm × 1 cm = 4 sq. cm
Area of the rectangle IV = length × breadth
= 3 cm × 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 have

Area of the rectangle I
= 3 cm × 1 cm = 3 sq. cm
Area of the rectangle II
= 3 cm × 1 cm = 3 sq. cm
Area of rectangle III
= 3 cm × 1 cm = 3 sq. cm
∴ Total area of the given figure = 3 sq. cm + 3 sq. cm + 3 sq. cm = 9 sq. cm

Ex 10.3 Class 6 Maths 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 have
Area of the rectangle I
= 12 cm × 2 cm = 24 sq. cm
Area of the rectangle II
= 8 cm × 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 have

Area of the rectangle I
= 7 cm × 7 cm = 49 sq. cm
Area of the rectangle II
= 21 cm × 7 cm = 147 sq. cm
Area of the rectangle III
= 7 cm × 7 cm = 49 sq. cm
∴ Total area of the whole figure
= 49 sq. cm + 147 sq. cm + 49 sq. cm
= 245 sq. cm

Area of first rectangle = 5 × 1 = 5 sq. cm

Area of second rectangle = 4 × 1 = 4 sq. cm

∴ Total area of the whole figure

= 5 sq. cm + 4 sq. cm = 9 sq. cm

Ex 10.3 Class 6 Maths 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:
Given: Length of the tile = 12 cm
Breadth of the tile = 5 cm
∴ Area of a tile = length × breadth = 12 cm × 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 × breadth = 144 cm × 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 rectangular region = 36 cm
∴ Area of the rectangular region = length × breadth = 70 cm × 36 cm = 2520 sq. cm
∴ Number of tiles needed to cover the whole rectangular region
= 2520 sq. cm ÷ 60 sq. cm
= 42 tiles

Related Links:

NCERT Solutions for Maths Class 7

NCERT Solutions for Maths Class 8

NCERT Solutions for Maths Class 9

NCERT Solutions for Maths Class 10

NCERT Solutions for Maths Class 11

NCERT Solutions for Maths Class 12