Mensuration
Exercise 10.3
EX 10.3 QUESTION 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
Solution:
(Area of rectangle = Length × Breadth)
(a) l = 3 cm and b = 4 cm
Area = length x breadth = 3 × 4
= 12 cm2
(b) l = 12 m and b = 21 m
Area = length x breadth = 12 × 21
= 252 m2
(c) l = 2 km and b = 3 km
Area = length x breadth = 2 × 3
= 6 km2
(d) l = 2 m and b = 70 cm = 0.70 m
Area = length x breadth = 2 × 0.70
= 1.40 m2
EX 10.3 QUESTION 2.
Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 m
Solution:
(a) Area of square = side2
= 102
= 100 cm2
(b) Area of square = side2
= 142
= 196 cm2
(c) Area of square = side2
= 52
=25 cm2
EX 10.3 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) 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
Area of rectangle 56 m2 i.e (c) is the largest area and area of rectangle 51 m2 i.e (b) is the smallest area.
EX 10.3 QUESTION 4.
The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.
Solution:
Area of rectangle = length × width
300 = 50 × width
width = 300 / 50
width = 6 m
∴ The width of the garden is 6 m
EX 10.3 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:
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
EX 10.3 QUESTION 6.
A table top measures 2 m by 1 m 50 cm. What is its area in square metres?
Solution:
Given
Length = 2m
Breadth = 1m 50 cm = 1.50 m
Area = length x breadth = 2 × 1.50
= 3 m2
EX 10.3 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 = 4m
Breadth = 3 m 50 cm = 3.50 m
Area = length x breadth = 4 × 3.50
=14 m2
EX 10.3 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:
Area of floor = length x breadth = 5 × 4
= 20 m2
Area of square carpet = 3 × 3
= 9 m2
Area of floor that is not carpeted = 20 – 9
= 11 m2
∴ Area of the floor that is not carpeted is 11 m2
EX 10.3 QUESTION 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?
Solution:
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
∴ Remaining part of the land is 15 m2
EX 10.3 QUESTION 10.
By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).
Solution:
Area of the rectangle I = length x breadth
= 4 cm x 3 cm = 12 sq cm
Area of the rectangle II = length x breadth
= 3 cm x 2 cm = 6 sq cm.
Area of the rectangle III = length x breadth
= 4 cm x 1 cm = 4 sq cm
Area of the rectangle IV = length x breadth
= 3 cm x 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)
Area of the rectangle I
= 12 cm x 2 cm = 24 sq cm
Area of the rectangle II
= 8 cm x 2 cm = 16 sq cm
Area of rectangle III
= 3 cm x 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 QUESTION 11.
Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)
Solution:
(a)
Total area of the figure = 12 × 2 + 8 × 2
= 40 cm2
(b)
Area of the rectangle I
= 7 cm x 7 cm = 49 sq cm
Area of the rectangle II
= 21 cm x 7 cm = 147 sq cm
Area of the rectangle III
= 7 cm x 7 cm = 49 sq cm
∴ Total area of the whole figure
= 49 sq cm + 147 sq cm + 49 sq cm
= 245 sq cm.
(c)
Area of a rectangle = 2 × 1
= 2 cm2
Area of b rectangle = 2 × 1
= 2 cm2
Area of c rectangle = 5 × 1
= 5 cm2
Total area = 2 + 2 + 5
= 9 cm2
EX 10.3 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:
(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.
