NCERT Solutions for Class 6 Maths Chapter 10 Mensuration

Q.1 Find the areas of the following figures by counting square:

Answer :

(a) Number of full squares = 9
Area of 1 square = 1 sq unit
\(\therefore \)Area of 9 squares = 9 x 1 sq unit
= 9 sq units.
So, the area of the portion covered by 9 squares = 9 sq units
(b) Number of full squares = 5
\(\therefore \) Area of the figure = 5 x 1 sq unit = 5 sq units
(c) Number of full squares = 2
Number of half squares = 4
\(\therefore \) Area of the covered figure
= 2 x 1 + 4 x \(\frac{1}{2} \) = 2 + 2 = 4 sq units
(d) Number of full squares = 8
\(\therefore \) Area of the covered portion of the figure
= 8 x 1 sq unit = 8 sq units.

(e) Number of full squares = 10
Area covered by the figure = 10 x 1 sq unit = 10 sq units.
(f) Number of full squares = 2
Number of half squares = 4
\(\therefore \) Area of the covered figure
= (2 x 1 + 4 x \(\frac{1}{2} \))= (2 + 2) sq units = 4 sq units.
(g) Number of full squares = 4
Number of half squares = 4
\(\therefore \) Area of the covered figure = (4 x 1 + 4 x 12)
= (4 + 2) sq units = 6 sq units.

(h) Number of full squares = 5
\(\therefore \) Area of the covered figure
= 5 x 1 sq unit = 5 sq units.

(i) Number of full squares = 9
\(\therefore \) Area of the covered figure
= 9 x 1 sq units = 9 sq units.

(j) Number of full squares = 2
Number of half squares = 4
\(\therefore \) Area of the covered figure
=(2 x 1 + 4 x \(\frac{1}{2} \)) sq units
= (2 + 2) sq units = 4 sq units.
(k) Number of full squares = 4
Number of half squares = 2
\(\therefore \) Area of the covered figure
= (4 x 1 + 2 x \(\frac{1}{2} \))sq units
= (4 + 1)sq units = 5sq units

(l) Number of full squares = 4
Number of squares more than half = 3
Number of half squares = 2
\(\therefore \) Area of the covered figure
= (4 x 1 + 3 x 1 + 2 x \(\frac{1}{2} \) sq units
= (4 + 3 + 1) sq units = 8 sq units.

(m) Number of full squares = 6
Number of more than half squares = 8
Area of the covered figure = (6 x 1 + 8 x 1) sq units
= (6 + 8) sq units = 14 sq units.
(n) Number of full squares = 9
Number of more than half squares = 9
\(\therefore \) Area of the covered figure
= (9 x 1 + 9 x 1) sq units = (9 + 9) sq units = 18 sq units.

Q.1 Find the area 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

Answer :

Area of rectangle = Length × Breadth
(a) l = 3 cm and b = 4 cm
Area = l × b = 3 × 4 = 12 \( cm^2 \)
(b) l = 12 m and b = 21 m
Area = l × b = 12 × 21
= 252 \( m^2 \)
(c) l = 2 km and b = 3 km
Area = l × b = 2 × 3
= 6 \( km^2 \)
(d) l = 2 m and b = 70 cm = 0.70 m
Area = l × b = 2 × 0.70
= 1.40 \( m^2 \)

Q.2 Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 m

Answer :

(a) Area of square = \( side^2 \)
= \( 10^2 = 100 cm^2 \)
(b) Area of square =\( side^2 \) \( = 14^2 = 196 cm^2 \)
(c) Area of square = \(side^2 \)
\( = 5^2 = 25 cm^2 \)

Q.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?

Answer :

(a) Area of rectangle = l × b
\(= 9 × 6 = 54 m^2 \)
(b) Area of rectangle = l × b
\( = 17 × 3 = 51 m^2 \)
(c) Area of rectangle = l × b
\( = 4 × 14 = 56 m^2 \)
Area of rectangle 56 \( m^2 \) i.e (c) is the largest area and area of rectangle 51 \( m^2 \) i.e (b) is the smallest area

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

Answer :

Area of rectangle = length × width
300 = 50 × width
width = 300 / 50
width = 6 m

Q.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.?

Answer :

Area of land = length × breadth
\( = 500 × 200 = 1,00,000 m^2 \)
Cost of tiling 1,00,000 sq m of land = (8 × 1,00,000) / 100
= Rs 8000

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

Answer :

l = 2m
b = 1m 50 cm = 1.50 m
Area = l × b = 2 × 1.50
\(= 3 m^2\)

Q.7 A room is 4 m long and 3 m 50 cm wide. Howe many square metres of carpet is needed to cover the floor of the room?

Answer :

l = 4m
b = 3 m 50 cm = 3.50 m
Area = l × b = 4 × 3.50
=14 \(m^2 \)

Q.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.

Answer :

Area of floor = l × b = 5 × 4
\(= 20 m^2 \)
Area of square carpet = 3 × 3
\(= 9 m^2 \)
Area of floor that is not carpeted = 20 – 9
\(= 11 m^2 \)

Q.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?

Answer :

Area of flower square bed = 1 × 1
\(= 1 m^2 \)
Area of 5 square bed = 1 × 5
\(= 5 m^2 \)
Area of land = 5 × 4
\(= 20 m^2 \)
Remaining part of the land = Area of land – Area of 5 square bed
\(= 20 – 5 = 15 m^2 \)

Q.10 By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).

Answer :

(a) Area of HKLM = 3 x 3 =\( 9 cm^2\)
Area of IJGH = 1 x 2 = 2 \(cm^2\)
Area of FEDG = 3 x 3 = 9 \(cm^2\)
Area of ABCD = 2 x 4 = 8 \(cm^2\)
Total area of the figure = 9 + 2 + 9 + 8 = 28 \(cm^2\)
(b) Area of ABCD = 3 x 1 = 3 \(cm^2\)
Area of BDEF = 3 x 1 = 3 \(cm^2\)
Area of FGHI = 3 x 1 = 3 \(cm^2\)
Total area of the figure = 3 + 3 + 3 = 9 \(cm^2\)

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

Answer :

(a) Area of rectangle ABCD = 2 x 10 = 20 \(cm^2 \)
Area of rectangle DEFG = 10 x 2 = 20 \(cm^2 \)
Total area of the figure = 20 + 20 = 40 \(cm^2 \)

(b) There are 5 squares each of side 7 cm.
Area of one square = 7 x 7 = 49\(cm^2 \)
Area of 5 squares = 49 x 5 = 245 \(cm^2 \)
(c) Area of rectangle ABCD = 5 x 1 = 5 \(cm^2 \)
Area of rectangle EFGH = 4 x 1 = 4 \(cm^2 \)
Total area of the figure = 5 + 4 \(cm^2 \)

Q.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

Answer :

(a) Area of rectangle = 100 × 144
= 14400 cm
Area of one tile = 5 × 12
\(= 60 cm^2 \)
Number of tiles = \(\frac{(Area of rectangle)}{(Area of one tile)} \)
\(= \frac{14400}{60} \) = 240
Hence, 240 tiles are needed
(b) Area of rectangle = 70 × 36
\(= 2520 cm^2 \)
Area of one tile = 5 × 12
\(= 60 cm^2 \)
Number of tiles = \(\frac{(Area of rectangle)}{(Area of one tile)} \)
=\(\frac{2520}{60} = 42 \)