Mensuration
Exercise 10.3
1). 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
Solution:
(a) 3 cm and 4 cm
Given: length = 3 cm
breadth = 4 cm
Area of rectangle = length X breadth
= 3 X 4
= 12 cm2
(b) 12 m and 21 m
Given: length = 12 m
breadth = 21 m
Area of rectangle = length X breadth
= 12 X 21
= 252 m2
(c) 2 km and 3 km
Given: length = 2 km
breadth = 3 km
Area of rectangle = length X breadth
= 2 X 3
= 6 km2
(d) 2 m and 70 cm
Given: length = 2 m
breadth = 70 cm = 0.70 m
Area of rectangle = length X breadth
= 2 X 0.70
= 1.40 m2
2). Find the areas of the squares whose sides are:
(a) 10 cm (b) 14 cm (c) 5 m
Solution:
(a) 10 cm
Given: side = 10 cm
Area of square = side X side
= 10 X 10
= 100 cm2
(b) 14 cm
Given: side = 14 cm
Area of square = side X side
= 14 X 14
= 196 cm2
(c) 5 m
Given: side = 5 m
Area of square = side X side
= 52
= 5 X 5
= 25 m2
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?
Solution:
(a) 9 m and 6 m
Given: length = 9 m
breadth = 6 m
Area of rectangle = length X breadth
= 9 X 9
= 54 m2
(b) 17 m and 3 m
Given: length = 17 m
breadth = 3 m
Area of rectangle = length X breadth
= 17 X 3
= 51 m2
(c) 4 m and 14 m
Given: length = 4 m
breadth = 14 m
Area of rectangle = length X breadth
= 4 X 14
=56 m2
Ans: rectangle b has the smallest area and rectangle c has the largest area.
4). The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.
Given: length of the rectangular garden = 50 m
Area of the rectangular garden = 300 sq m
To find: Breadth of the garden = ?
Area of garden = length X breadth
300 = 50 X breadth
50 X breadth = 300
Breadth = 300 ÷ 50
=6 m
Ans: breadth of the garden = 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.?
Given: length of the rectangular plot = 500 m
breadth of the plot = 200 m
rate of tilling the plot = ₹ 8 per hundred sq m
to find: Cost of the tilling the plot = ?
Area of plot = length X breadth
= 500 X 200
= 100000 m2
Cost of tilling = Rate X Area
= (8/ 100) X 100000
= (8 X 100000) ÷ 100
= 800000 ÷ 100
= 8000
Ans: cost of tilling the plot = ₹ 8000
6). A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?
Given: length of the table top= 2 m
Breadth of the table top = 1 m 50 cm = 1.50 m
Area of table top = length X breadth
= 2 X 1.50
=3.00 m2
Ans: area of the table-top = 3 m2
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?
Given: length of the room = 4 m
breadth of the room = 3 m 50 cm = 3.50 m
Area of room = length X breadth
= 4 X 3.50
=14.00 m2
Ans: carpet needed to cover the floor = 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.
Given: length of the floor = 5 m
Breadth of the floor = 4 m
Side of the square carpet = 3 m
Area of the floor = length X breadth
= 5 X 4
=20 m2
Area of the carpet = side2
= 32
= 9 m2
Area of the floor not carpeted = Area of the floor – area of the carpet
= 20 – 9
= 11
Ans: Area of the floor not carpeted = 9 m2
9). Five square flower beds each of side 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?
Given: length of the land = 5 m
Breadth of the land = 4 m
Side of the square flower blade = 1 m
Area of the floor = length X breadth
= 5 X 4
=20 m2
Area of square = side X side
= 1 m2
Area of the 5 flower beds = 5 X 1
= 5 m2
Area of the remaining part of the land = Area of the land
– area of 5 flower beds
= 20 – 5
= 15
Ans: Area of the remaining part of the land = 15 m2
10). By splitting the following figures into rectangles, find their areas
(The measures are given in centimetres).
For Rectangle 1
Given: length = 2 cm
breadth = 1 cm
Area of rectangle = length X breadth
= 2 X 1
= 2 cm2
For rectangle 2
Given: length = 5 cm
breadth = 1 cm
Area of rectangle = length X breadth
= 5 X 1
= 5 cm2
For rectangle 3
Given: length = 2 cm
breadth = 1 cm
Area of rectangle = length X breadth
= 2 X 1
= 2 cm2
Area of the figure = 5 + 2 + 2
= 9 cm2
11). Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)
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) 100 cm and 144 cm
Length = 100 cm
Breadth = 144 cm
Area of rectangle = length X breadth
= 100 X 144
= 14400 cm2
Length of the tile = 12 cm
breadth of the tile = 5 cm
Area of the tile = length X breadth
= 12 X 5
= 60 cm2
Number of tiles = area of the region
area of the tile
= 14400/60
= 240
(b) 70 cm and 36 cm.
Length = 70 cm
Breadth = 36 cm
Area of rectangle = length X breadth
= 70 X 36
= 2520 cm2
Length of the tile = 12 cm
breadth of the tile = 5 cm
Area of the tile = length X breadth
= 12 X 5
= 60 cm2
Number of tiles = area of the region
area of the tile
= 2520/60
=42
Click here for the solutions of
Chapter 10 Mensuration
Chapter 8 Decimals
Chapter 7 Fractions
Chapter 6 Integers
Chapter 5 Understanding Elementary Shapes
Chapter 4 Basic Geometrical Ideas
Chapter 3: Playing With Numbers
Chapter 2: Whole Numbers
Chapter 1: Knowing Our Numbers
