Well-designed AP 6th Class Maths Guide Chapter 10 Mensuration Exercise 10.3 offers step-by-step explanations to help students understand problem-solving strategies.
Mensuration Class 6 Exercise 10.3 Solutions – 6th Class Maths 10.3 Exercise Solutions
Question 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) Length of the rectangle = 3 cm
Breadth of the rectangle = 4 cm
Area of the rectangle
= length × breadth
= 3 cm × 4 cm
= 12sq.cm
b) Length of the rectangle = 12 m
Breadth of the rectangle = 21 m
Area of the rectangle
= length × breadth
= 12 m × 21 m
= 252 sq.m
c) Length of the rectangle = 2 km
Breadth of the rectangle = 3 km
Area of the rectangle
= length × breadth
= 2 km × 3 km
= 6 sq. km.
d) Length of the rectangle = 2 m
Breadth of the rectangle = 70 cm
= 0.70 m
Area of the rectangle
= length × breadth
= 2 m × 0.70 m
= 1.40 sq.m
Question 2.
Find the areas of the squares whose sides are:
a) 10 cm
b) 14 cm
c) 5 m
Solution:
a) Side of the square = 10 cm
∴ Area of the square = side × side
= 10 cm × 10 cm
= 100 sq.cm
b) Side of the square = 14 cm
∴ Area of the square = side × side
= 14 cm × 14 cm
= 196 sq.cm
c) Side of the square = 5 m
∴ Area of the square
= side × side
= 5 m × 5 m
= 25 sq.m
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) Length of the rectangle = 9 m
Breadth of the rectangle = 6 m
∴ Area of the rectangle
= length × breadth
= 9 m × 6 m
= 54 sq.m.
b) Length of the rectangle = 17 m
Breadth of the rectangle = 3 m
∴ Area of the rectangle = length × breadth
= 17 m × 3 m
= 51 sq.m.
c) Length of the rectangle = 4 m
Breadth of the rectangle = 14 m
∴ Area of the rectangle = length × breadth
= 4 m × 14 m
= 56 sq.m.
From the above information
Rectangle (c) has the largest area i.e., 56 sq.m and rectangle
(b) has smallest area i.e. 51 sq.m
Question 4.
The area of a rectangular garden 50 m long is 300 sq m . Find the width of the garden.
Solution:
Length of the rectangular garden = 50 m
Area of the rectangular garden = 300 sq.m.
∴ Width of the rectangular garden = Area + Length
= 300 ÷ 50
= 6 m
∴ Width of the rectangular garden 1 m.
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:
Length of the rectangular plot = 500 m
and breadth = 200 m
Area of rectangular park
= length × breadth
= 500 m × 200 m
= 1,00,000 sq.m
Rate of the tiling the plot = ₹8 per 100 sq.m.
∴ Cost of tiling the garden = 100000 × \(\frac { 8 }{ 106 }\) =₹ 8000
Hence the cost of tiling the rectangular plot = ₹ 8000
Question 6.
A table-top measures 2 m by 1 m 50 cm . What is its area in square metres ?
Solution:
Length of the table – top = 2 m
and its breadth = 1 m 50 cm = 1.50 m
Area of the table top = length × breadth
= 2 m × 1.50 m = 3 m2
Hence, the area of the table top = 3m2 (or) 3 sq.m.
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:
Length of the room = 4 m
Breadth of the room =3.5 m
Area of the room = length × breadth
= 4 m × 3.5 m
= 14 m2 (or) 14 sq.m
Hence, the area of the carpet needed = 14sq.m
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:
Length of the floor = 5 m
Breadth of the floor = 4m
∴ Area of the floor = length × breadth
= 5 m × 4 m
= 20 sq.m
Side of the square carpet = 3 m
∴ Area of the square carpet = side × side
= 3 m × 3 m
= 9 sq.m
∴ Area of the floor which is not carpeted
= Area of floor – Area of square carpet
= 20 m2 – 9m2
= 11 sq.m.
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:
Side of the square flower bed = 1m
∴ Area of a square flower bed
= side × side
= 1 m × 1 m
= 1 sq.m
So, area of 5 square flower beds = 5 × 1 sq.m = 5
Now, Length of the land = 5 m
Breadth of the land = 4 m
Area of the land = length × breadth = 5 m × 4 m = 20 sq.m.
∴ Area of the remaining part = Area of land – Area of 5 square flower beds.
= 20 sq.m – 5 sq.m = 15 sq.m
Question 10.
By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).
Solution:
a) Splitting the given figure into four rectangles, they are I, II, II and IV
Area of the rectangle I
= length × breadth
= 4 cm × 3 cm
= 12 sq.m
Area of the rectangle II
= 3 cm × 2 cm
= 6 sq.m
Area of the rectangle III
= 4 cm × 1 cm
= 4 sq.cm
Area of the rectangle IV
= 3 cm × 2 cm
= 6 sq. cm
Total area of the given figure = 12 sq.cm + 6 sq.cm + 4 sq.cm + 6 sq.cm = 28 sq.cm
b) Splitting the given figure into three rectangles, they are I, II and III
Area of the Rectangle I = length × breadth
= 3 cm × 1 cm
= 3 sq.cm
Area of the rectangle II
= 3 cm × 1 cm
= 3 sq.m
Area of the rectangle III
= 3 cm × 1 cm = 3 sq.cm
∴ Total area of the given figure = 3 sq.cm + 3 sq.cm + 3 sq.cm = 9 sq.cm
Question 11.
Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)
Solution:
a) Splitting the given figure into two rectangles, they are I and II
Now, area of the rectangle I
= length × breadth
= 10 cm × 2 cm
= 20 sq.cm
Area of the rectangle II
= 10 cm × 2 cm
= 20 sq.cm
∴ Total area of the given figure
= 20 sq.cm + 20 sq.cm
= 40 sq.cm
b) Splitting the given figure into two squares, and one rectangle, they are I and III are squares and il is rectangle.
Now, Area of the square l = side × side = 7 cm × 7 cm = 49 sq.cm
Area of the rectangle II = length × breadth
= 21 cm × 7 cm
= 147 sq.cm
Area of the square III
= 7 cm × 7 cm
= 49 sq.cm
∴ Total area of the given figure = 49 sq.cm + 147 sq.cm + 49 sq.cm
= 245 sq.cm
c) Splitting the given figure into two rectangles, they are I and II
Area of the rectangle I = length × breadth
= 4 cm × 1 cm
= 4 sq.cm
Area of the rectangle II = 5 cm × 1 cm
= 5 sq.cm
∴ Total area of the given figure = 4 sq.cm + 5 sq.cm
= 9 sq.cm
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:
Length of the tile = 12 cm.
Breadth-of the tile = 5 cm.
∴ Area of the tile = length × breadth = 12 cm × 5 cm = 60 sq.cm.
Now
a) Length of the rectangular region = 100 cm
Breadth of the region = 144 cm
∴ Area of the rectangular region = length × breadth
= 100 cm × 144 cm
= 14400 sq.cm.
∴ Number of tiles needed to cover the whole rectangular region = 14400 sq.cm ÷ 60 sq.cm = 240 tiles
b) Length of the rectangular region = 70 cm
Breadth of the rectangular region = 36 cm
Area of the rectangular region = length × breadth
= 70 cm × 36 cm
= 2520 sq.cm
∴ Number of tiles needed to cover the whole rectangular region
= 2520 sq.cm ÷ 60 sq.cm = 42 tiles.