NCERT Solutions for Class 6 Maths - Mensuration (Exercise 10.2 and 10.3)

Exercise 10.2

Q1. Find the areas of the following figures by counting squares:

(a)

(b)  

(c)  

(d)  

(e)  

(f)  

(g)  

(h)  

(i)  

(j)  

(k)  

(l)  

(m)  

(n)  

Ans:
(a) Number of filled square = 9
∴ Area covered by squares = 9 x 1 = 9 sq. units

(b) Number of filled squares = 5
∴ Area covered by filled squares = 5 x 1 = 5 sq. units

(c) Number of full filled squares = 2
Number of half-filled squares = 4
∴ Area covered by full filled squares = 2 x 1 = 2 sq. units
And Area covered by half-filled squares  =
∴ Total area = 2 + 2 = 4 sq. units

(d) Number of filled squares = 8
∴ Area covered by filled squares = 8 x 1 = 8 sq. units

(e) Number of filled squares = 10
∴ Area covered by filled squares = 10 x 1 = 10 sq. units

(f) Number of full filled squares = 2
Number of half-filled squares = 4
∴ Area covered by full filled squares = 2 x 1 = 2 sq. units
And Area covered by half-filled squares  =
∴ Total area = 2 + 2 = 4 sq. units

(g) Number of full filled squares = 4
Number of half-filled squares = 4
∴ Area covered by full filled squares = 4 x 1 = 4 sq. units
And Area covered by half-filled squares  =
∴ Total area = 4 + 2 = 6 sq. units

(h) Number of filled squares = 5
∴ Area covered by filled squares = 5 x 1 = 5 sq. units

(i) Number of filled squares = 9
∴ Area covered by filled squares = 9 x 1 = 9 sq. units

(j) Number of full filled squares = 2
Number of half-filled squares = 4
∴ Area covered by full filled squares = 2 x 1 = 2 sq. units
And Area covered by half-filled squares  =
∴ Total area = 2 + 2 = 4 sq. units

(k) Number of full filled squares = 4
Number of half-filled squares = 2
∴ Area covered by full filled squares = 4 x 1 = 4 sq. units
And Area covered by half-filled squares    
∴ Total area = 4 + 1 = 5 sq. units

(l) Number of full filled squares = 3
Number of half-filled squares = 10
∴ Area covered by full filled squares = 3 x 1 = 3 sq. units
And Area covered by half-filled squares  
∴ Total area = 3 + 5 = 8 sq. units

(m) Number of full filled squares = 7
Number of half-filled squares = 14
∴ Area covered by full filled squares = 7 x 1 = 7 sq. units
And Area covered by half-filled squares  
∴ Total area = 7 + 7 = 14 sq. units

(n) Number of full filled squares = 10
Number of half-filled squares = 16
∴ Area covered by full filled squares = 10 x 1 = 10 sq. units
And Area covered by half-filled squares  
∴ Total area = 10 + 8 = 18 sq. units

Q1. 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
Ans:
(a) Area of rectangle = length x breadth
= 3 cm x 4 cm = 12 cm² 
(b) Area of rectangle = length x breadth
= 12 m x 21 m = 252 m² 

(c) Area of rectangle = length x breadth
= 2 km x 3 km = 6 km² 

(d) Area of rectangle = length x breadth
= 2 m x 70 cm
= 2 m x 0.7 m = 1.4 m² 

Q2. Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 m
Ans:
(a) Area of square = side x side = 10 cm x 10 cm = 100 cm²
(b) Area of square = side x side = 14 cm x 14 cm = 196 cm²
(c) Area of square = side x side = 5 m x 5 m = 25 m²

Q3. 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?
Ans: 
(a) Area of rectangle = length x breadth = 9 m x 6 m = 54 m² 
(b) Area of rectangle = length x breadth= 3 m x 17 m = 51 m² 
(c) Area of rectangle = length x breadth= 4 m x 14 m = 56 m² 
Thus, the rectangle (c) has largest area, and rectangle (b) has smallest area.

Q4. The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.
Ans:Length of rectangle = 50 m and Area of rectangle = 300 m²
Since, Area of rectangle = length x breadth
Therefore,
Thus, the breadth of the garden is 6 m.

Q5. 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?
Ans: Length of land = 500 m and Breadth of land = 200 m
Area of land = length x breadth = 500 m x 200 m = 1,00,000 m²
Cost of tilling 100 sq. m of land = 8
∴ Cost of tilling 1,00,000 sq. m of land =   =  8000

Q6. A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?
Ans: Length of table = 2 m
Breadth of table = 1 m 50 cm = 1.50 m
Area of table = length x breadth
= 2 m x 1.50 m = 3 m²

Q7. 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?
Ans: Length of room = 4 m
Breadth of room = 3 m 50 cm = 3.50 m
Area of carpet = length x breadth
= 4 x 3.50 = 14m²

Q8: 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.
Ans: Length of floor = 5 m and breadth of floor = 4 m
Area of floor = length x breadth
= 5 m x 4 m = 20 m² Now, Side of square carpet = 3 m
Area of square carpet = side x side = 3 x 3 = 9 m²
Area of floor that is not carpeted = 20 m² – 9 m² = 11 m²

Q9. 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?
Ans: Side of square bed = 1 m
Area of square bed = side x side = 1 m x 1 m = 1 m²
∴ Area of 5 square beds = 1 x 5 = 5 m²
Now, Length of land = 5 m
Breadth of land = 4 m
∴ Area of land = length x breadth = 5 m x 4 m = 20 m²
Area of remaining part = Area of land – Area of 5 flower beds
= 20 m² – 5 m² = 15 m²

Q10. By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).


Ans:
(a)

Area of HKLM = 3 x 3 = 9 cm²
Area of IJGH = 1 x 2 = 2 cm²
Area of FEDG = 3 x 3 = 9 cm² 
Area of ABCD = 2 x 4 = 8 cm²
Total area of the figure = 9 + 2 + 9 + 8 = 28 cm² 
(b)

Area of ABCD = 3 x 1 = 3 cm²
Area of BDEF = 3 x 1 = 3 cm²
Area of FGHI = 3 x 1 = 3 cm²
Total area of the figure = 3 + 3 + 3 = 9 cm²

Q11. Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)

Ans: 
(a) 

Area of rectangle ABCD = 2 x 10 = 20 cm²
Area of rectangle DEFG = 10 x 2 = 20 cm²
Total area of the figure = 20 + 20 = 40 cm²
(b) 

There are 5 squares.
Each side is 7 cm
Area of 5 squares = 5 × 7²
= 245 cm²
(c) 

Area of rectangle ABCD = 5 x 1 = 5 cm² 
Area of rectangle EFGH = 4 x 1 = 4 cm² 
Total area of the figure = 5 + 4 cm² 

Q12. 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
Ans:
(a) Area of region = 100 cm x 144 cm = 14400 cm²
Area of one tile = 5 cm x 12 cm = 60 cm²

Thus, 240 tiles are required.
(b) Area of region = 70 cm x 36 cm = 2520 cm²
Area of one tile = 5 cm x 12 cm = 60 cm²

Thus, 42 tiles are required.