Class 6 - Mathematics : Mensuration
Exercise : 10.3
Top Block 1
NCERT Solutions Class 6 Mathematics Mensuration Ex 10.3
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
Answer :
(a) Area of rectangle = length x breadth
= 3 cm x 4 cm = 12 cm2
(b) Area of rectangle = length x breadth
= 12 m x 21 m = 252 m2
(c) Area of rectangle = length x breadth
= 2 km x 3 km = 6 km2
(d) Area of rectangle = length x breadth
= 2 m x 70 cm = 2 m x 0.7 m = 1.4 m2
Question: 2.Find the areas of the squares whose sides are:
(a) 10 cm
(b) 14 cm
(c) 5 cm
Answer :
(a) Area of square = side x side = 10 cm x 10 cm = 100 cm2
(b) Area of square = side x side = 14 cm x 14 cm = 196 cm2
(c) Area of square = side x side = 5 m x 5 m = 25 m2
Question: 3.The length and the 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?
Answer :
(a) Area of rectangle = length x breadth = 9 m x 6 m = 54 m2
(b) Area of rectangle = length x breadth= 3 m x 17 m = 51 m2
(c) Area of rectangle = length x breadth= 4 m x 14 m = 56 m2
Thus, the rectangle (c) has largest area, i.e. 56 m2 and rectangle (b) has smallest area, i.e., 56 m2.
Question: 4.The area of a rectangle garden 50 m long is 300 m2, find the width of the garden.
Answer :
Length of rectangle = 50 m and Area of rectangle = 300 m2
Since, Area of rectangle = length x breadth
Area of rectangle
Therefore, Breadth = ─────────── = 6 m
Length
Thus, the breadth of the garden is 6 m.
Question: 5.What is the cost of tilling a rectangular plot of land 500 m long and 200 m wide at the rate of Rs. 8 per hundred sq. m?
Answer :
Length of land = 500 m and Breadth of land = 200 m
Area of land = length x breadth = 500 m x 200 m = 1,00,000 m2
∵ Cost of tilling 100 sq. m of land = Rs. 8
∴ Cost of tilling 1,00,000 sq. m of land = = Rs. 8000
Question: 6.A table-top measures 2 m by 1 m 50 cm. What is its area in square meters?
Answer :
Length of table = 2 m and breadth of table = 1 m 50 cm = 1.50 m
Area of table = length x breadth
= 2 m x 1.50 m = 3 m2
Mddle block 1
Question: 7.A room us 4 m long and 3 m 50 cm wide. How many square meters of carpet is needed to cover the floor of the room?
Answer :
Length of room = 4 m and breadth of room = 3 m 50 cm = 3.50 m
Area of carpet = length x breadth
= 4 x 3.50 = 14m2
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.
Answer :
Length of floor = 5 m and breadth of floor = 4 m
Area of floor = length x breadth
= 5 m x 4 m = 20 m2
Now, Side of square carpet = 3 m
Area of square carpet = side x side = 3 x 3 = 9 m2
Area of floor that is not carpeted = 20 m2 – 9 m2 = 11 m2
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?
Answer :
Side of square bed = 1 m
Area of square bed = side x side = 1 m x 1 m = 1 m2
∴ Area of 5 square beds = 1 x 5 = 5 m2
Now, Length of land = 5 m and breadth of land = 4 m
∴ Area of land = length x breadth = 5 m x 4 m = 20 m2
Area of remaining part = Area of land – Area of 5 flower beds
= 20 m2 – 5 m2 = 15 m2
Question: 10.By splitting the following figures into rectangles, find their areas. (The measures are given in centimeters)
Answer :
(a) Area of HKLM = 3 x 3 = 9 cm2
Area of IJGH = 1 x 2 = 2 cm2
Area of FEDG = 3 x 3 = 9 cm2
Area of ABCD = 2 x 4 = 8 cm2
Total area of the figure = 9 + 2 + 9 + 8 = 28 cm2
Area of BDEF = 3 x 1 = 3 cm2
Area of FGHI = 3 x 1 = 3 cm2
Total area of the figure = 3 + 3 + 3 = 9 cm2
Question: 11.Split the following shapes into rectangles and find their areas. (The measures are given in centimeters)
Answer :
(a) Area of rectangle ABCD = 2 x 10 = 20 cm2
Area of rectangle DEFG = 10 x 2 = 20 cm2
Total area of the figure = 20 + 20 = 40 cm2
Area of one square = 7 x 7 = 49 cm2
Area of 5 squares = 49 x 5 = 245 cm2
Area of rectangle EFGH = 4 x 1 = 4 cm2
Total area of the figure = 5 + 4 cm2
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
Answer :
(a) Area of region = 100 cm x 144 cm = 14400 cm2
Area of one tile = 5 cm x 12 cm = 60 cm2
Area of region
Number of tiles = ────────── = 240
Area of one
Thus, 240 tiles are required.
(b) Area of region = 70 cm x 36 cm = 2520 cm2
Area of one tile = 5 cm x 12 cm = 60 cm2
Area of region
Number of tiles = ────────── = 42
Area of one
Thus, 42 tiles are required.