NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Exercise 10.3 discusses the key topics, including the important formulas and steps to be followed while determining the area of a rectangle and square. We also have a set of exemplar questions which will help students analyse the type of questions that would appear in the Class 6 annual exam. These NCERT Solutions Class 6 Maths will help students improve their problem-solving abilities, which are important from the exam point of view.
NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Exercise 10.3
Access NCERT Solutions for Class 6 Chapter 10: Mensuration Exercise 10.3
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
Solutions:
We know that
Area of rectangle = length × breadth
(a) l = 3 cm and b = 4 cm
Area = l × b = 3 × 4
= 12 cm2
(b) l = 12 m and b = 21 m
Area = l × b = 12 × 21
= 252 m2
(c) l = 2 km and b = 3 km
Area = l × b = 2 × 3
= 6 km2
(d) l = 2 m and b = 70 cm = 0.70 m
Area = l × b = 2 × 0.70
= 1.40 m2
2. Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 m
Solutions:
(a) Area of square = side2
= 102
= 100 cm2
(b) Area of square = side2
= 142
= 196 cm2
(c) Area of square = side2
= 52
=25 cm2
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?
Solutions:
(a) Area of rectangle = l × b
= 9 × 6
= 54 m2
(b) Area of rectangle = l × b
= 17 × 3
= 51 m2
(c) Area of rectangle = l × b
= 4 × 14
= 56 m2
Option (c), the rectangle with an area of 56 m2, has the largest area, and option (b), the rectangle with an area of 51 m2, has the smallest area.
4. The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.
Solutions:
Area of rectangle = length × width
300 = 50 × width
width = 300 / 50
width = 6 m
∴ The width of the garden is 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 100 sq m?
Solutions:
Area of land = length × breadth
= 500 × 200
= 1,00,000 m2
∴ Cost of tiling 1,00,000 sq m of land = (8 × 1,00,000) / 100
= ₹ 8000
6. A table top measures 2 m by 1 m 50 cm. What is its area in square metres?
Solutions:
Given
l = 2 m
b = 1 m 50 cm = 1.50 m
Area = l × b = 2 × 1.50
= 3 m2
7. A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet are needed to cover the floor of the room?
Solutions:
Given
l = 4m
b = 3 m 50 cm = 3.50 m
Area = l × b = 4 × 3.50
= 14 m2
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.
Solutions:
Area of floor = l × b = 5 × 4
= 20 m2
Area of square carpet = 3 × 3
= 9 m2
Area of floor that is not carpeted = 20 – 9
= 11 m2
∴ The area of the floor that is not carpeted is 11 m2.
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?
Solutions:
Area of flower square bed = 1 × 1
= 1 m2
Area of 5 square bed = 1 × 5
= 5 m2
Area of land = 5 × 4
= 20 m2
Remaining part of the land = Area of land – Area of 5 square bed
= 20 – 5
= 15 m2
∴ The remaining part of the land is 15 m2.
10. By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).
Solutions:
(a)
Area of yellow region = 3 × 3
= 9 cm2
Area of orange region = 1 × 2
= 2 cm2
Area of grey region = 3 × 3
= 9 cm2
Area of brown region = 2 × 4
= 8 cm2
Total area = 9 + 2 + 9 + 8
= 28 cm2
∴ The total area is 28 cm2.
(b)
Area of brown region = 3 × 1
= 3 cm2
Area of orange region = 3 × 1
= 3 cm2
Area of grey region = 3 × 1
= 3 cm2
Total area = 3 + 3 + 3
= 9 cm2
∴ The total area is 9 cm2.
11. Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)
Solutions:
(a)
Total area of the figure = 12 × 2 + 8 × 2
= 40 cm2
(b)
There are 5 squares, and each side is 7 cm.
Area of 5 squares = 5 × 72
= 245 cm2
(c)
Area of grey rectangle = 2 × 1
= 2 cm2
Area of brown rectangle = 2 × 1
= 2 cm2
Area of orange rectangle = 5 × 1
= 5 cm2
Total area = 2 + 2 + 5
= 9 cm2
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?
Solutions:
(a) Area of rectangle = 100 × 144
= 14400 cm
Area of one tile = 5 × 12
= 60 cm2
Number of tiles = (Area of rectangle) / (Area of one tile)
= 14400 / 60
= 240
Hence, 240 tiles are needed.
(b) Area of rectangle = 70 × 36
= 2520 cm2
Area of one tile = 5 × 12
= 60 cm2
Number of tiles = (Area of rectangle) / (Area of one tile)
= 2520 / 60
= 42
Hence, 42 tiles are needed.
Also, explore –
NCERT Solutions for Class 6 Maths Chapter 10
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