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:
Area of rectangle = Length × Breadth
(a) l = 3 cm and b = 4 cm
Area = l × b = 3 × 4
= 12 \(\text{cm}^2\)
(b) l = 12 m and b = 21 m
Area = l × b = 12 × 21
= 252 \(\text{m}^2\)
(c) l = 2 km and b = 3 km
Area = l × b = 2 × 3
= 6 \(\text{km}^2\)
(d) l = 2 m and b = 70 cm = 0.70 m
Area = l × b = 2 × 0.70
= 1.40 \(\text{m}^2\)
2. Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 m
Solutions:
(a) Area of square = \(\text{side}^2\)
\(= 10^2\)
= 100 \(\text{cm}^2\)
(b) Area of square = \(\text{side}^2\)
= 142
= 196 \(\text{cm}^2\)
(c) Area of square = \(\text{side}^2\)
= 52
=25 \(\text{cm}^2\)
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 \(\text{m}^2\)
(b) Area of rectangle = l × b
= 17 × 3
= 51 \(\text{m}^2\)
(c) Area of rectangle = l × b
= 4 × 14
= 56 \(\text{m}^2\)
The area of rectangle 56 \(\text{m}^2\), i.e. (c), is the largest area and the area of rectangle 51 \(\text{m}^2\), i.e. (b), is 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 = \({300 \over 50}\)
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 hundred sq m?
Solutions:
Area of land = length × breadth
= 500 × 200
= 1,00,000 \(\text{m}^2\)
∴ Cost of tiling 1,00,000 sq m of land = \({(8 × 1,00,000)}\over 100}\)
= ₹ 8000
∴ The cost of tiling a rectangular plot of land is ₹ 8000.
6. A tabletop measures 2 m by 1 m 50 cm. What is its area in square metres?
Solutions:
l = 2m
b = 1m 50 cm = 1.50 m
Area = l × b = 2 × 1.50
= 3 \(\text{m}^2\)
∴ The area of the tabletop is 3 \(\text{m}^2\).
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:
l = 4m
b = 3 m 50 cm = 3.50 m
Area = l × b = 4 × 3.50
= 14 \(\text{m}^2\)
∴ The carpet required to cover the floor is 14 \(\text{m}^2\).
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 \(\text{m}^2\)
Area of square carpet = 3 × 3
= 9 \(\text{m}^2\)
Area of floor that is not carpeted = 20 – 9
= 11 \(\text{m}^2\)
∴ The area of the floor that is not carpeted is 11 \(\text{m}^2\).
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 \(\text{m}^2\)
Area of 5 square bed = 1 × 5
= 5 \(\text{m}^2\)
Area of land = 5 × 4
= 20 \(\text{m}^2\)
Remaining part of the land = Area of land – Area of 5 square bed
= 20 – 5
= 15 \(\text{m}^2\)
∴ The remaining part of the land is 15 \(\text{m}^2\).
10. By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).
(a)Area of yellow region = 3 × 3 = 9 \(\text{cm}^2\)
Area of orange region = 1× 2 = 2 \(\text{cm}^2\)
Area of grey region = 3 × 3 = 9 \(\text{cm}^2\)
Area of brown region = 2 × 4 = 8 \(\text{cm}^2\)
Total area = 9 + 2 + 9 + 8
= 28 \(\text{cm}^2\)
∴ The total area is 28 \(\text{cm}^2\).
(b)Area of brown region = 3 × 1
= 3 \(\text{cm}^2\)
Area of orange region = 3 × 1
= 3 \(\text{cm}^2\)
Area of grey region = 3 × 1
= 3 \(\text{cm}^2\)
Total area = 3 + 3 + 3
= 9 \(\text{cm}^2\)
∴ 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 \(\text{cm}^2\)
(b)
There are 5 squares, and each side is 7 cm.
Area of 5 squares = 5 × 72
= 245 \(\text{cm}^2\)
(c)
Area of grey rectangle = 2 × 1
= 2 \(\text{cm}^2\)
Area of brown rectangle = 2 × 1
= 2 \(\text{cm}^2\)
Area of orange rectangle = 5 × 1
= 5 \(\text{cm}^2\)
Total area = 2 + 2 + 5
= 9 \(\text{cm}^2\)
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 \(\text{cm}^2\)
Area of one tile = 5 × 12
= 60 \(\text{cm}^2\)
Number of tiles = \text{(Area of rectangle)} \over \text{(Area of one tile)}\)
\(= {14400 \over 60}\)
= 240
Hence, 240 tiles are needed
(b) Area of rectangle = 70 × 36
= 2520 \(\text{cm}^2\)
Area of one tile = 5 × 12
= 60 \(\text{cm}^2\)
Number of tiles = \text{(Area of rectangle)} \over \text{(Area of one tile)}\)
= \({2520 \over 60})\)
= 42
Hence, 42 tiles are needed.
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