ML Aggarwal CBSE Solutions Class 6 Math 11th Chapter Mensuration Exercise 11.2
Exercise 11.2
(1) Find the area of the region enclosed by the following figures by counting squares:
(i) The given figure is covered by complete squares only.
Number of complete covered squares = 9.
Area covered by complete square = (9 x 1) sq. unit = 9 sq. units
∴ Area of the region enclosed by the figure = 9 sq. units.
(ii) The given squares is covered by complete squares only.
Number of complete covered squares = = 5
Area covered by complete square = (5 x 1) sq. unit = 5 sq. unit.
∴ Area of the region enclosed by the figure = 5 sq. units.
(iii) The given figure is covered by complete squares only.
Number of complete square = 10.
Area covered by complete square = (10 x 1) = 10 sq. unit.
∴ Area of the region enclosed by the figure = 10 sq. units.
(iv) Number of complete covered squares = 4
Number of exactly half covered squares = 4
Area covered by complete squares = (4 x 1) sq units = 4 sq. units.
Area covered by exactly half covered squares = (4 x ½) = 2 square units.
∴ Area of the region enclosed by the given figure = (4 + 2) square units = 6 sq. units.
(v) Number of complete covered squares = 2
Number of exactly half covered squares = 4
Area covered by complete squares = (2 x 1) = 2 sq. units.
Area covered by exactly half covered squares = (4 x ½) = 2 square units
∴ Area of the region enclosed by the given figure = (2 + 2) sq. units = 4 sq. units.
(vi) Number of complete covered squares = 3
Number of exactly half covered squares = 6
Area covered by complete covered squares = (3 x 1) sq. units = 3 sq. units.
Area covered by exactly half covered squares = (6 x ½) = 3 sq. units
∴ Area of the region enclosed by the given figure = (3 + 3) sq. units = 6 sq. units.
(2) Find the area of the following closed figures by counting squares:
(i) Number of complete covered squares = 4
Number of more than half covered squares = 4
And, there is no exactly half squares covered.
So, estimate area of the given closed figure = (4 + 4) sq. units = 8 sq. units.
(ii) Number of complete covered squares = 7
Number of more than half covered squares = 6
And there is no exactly half covered squares covered.
So, estimate area of the given closed figure = (7 + 6) 13 sq units.
(iii) Number of complete covered squares = 11
Number of more than half covered squares = 7
And there is no exactly half covered squares covered.
So, estimate area of the given closed figure = (11 + 7) sq. units = 18 sq. units.
(3) Find the area:
(i) 9 m and 6 m
Solution: The area of rectangle = 9 m x 6 m
= 54 m2
(ii) 17 m and 3 m
Solution: The area of rectangle = 17 m x 3 m
= 51 m square.
(iii) 14 m and 4 m
Solution: The area of rectangle = 14 m x 4 m
= 56 meter square.
Here, No. iii) 14 m and 4 m is the largest area and No. ii) 17 m and 3 m is the smallest area.
(4) Find the areas of the rectangles whose two adjacent sides are:
(i) 14 cm and 23 cm
Solution: The area of rectangle = 14 cm x 23 cm
= 322 cm2
(ii) 3 km and 4 km
Solution: The area of rectangle = 3 km x 4 km = 12 km2
(iii) 2 m and 90 m
Solution: The area of rectangle = 2 m x 90 m = 180 m2
(5) Find area of squares whose sides are:
(i) 8 cm
Solution: The area of square = (side)2
= (8 cm)2
= 64 cm2
(ii) 14 m
Solution: The area of square = (14 cm)2
= 196 cm2
(iii) 2 m 50 cm
Solution: 2 m 50 cm
= 2 x 100 + 50
= 200 + 50
= 250 cm
The area of square = (250 cm)2
= 62500 cm2
(6) A room is 4 m long and 3 m 25 cm wide. How many square meters of carpet is needed to cover the floor of the room.
Solution: The length of the room is 4 m
& The breadth of the rooms is 3 m 25 cm = 3 m + 25/100 m
= 3 m + 0.25 m
= 3.25 m
The square meter of carpet is needed to cover the floor = 4 m x 3.25 m = 13 m2
(7) What is the cost of tiling a rectangular field 500 m long and 200 m wide at the rate of Rs. 7.5 per hundred square metres?
Solution: Te area of rectangular field = 500 m x 200 m = 100000 m2
Total cost needed = 100000 x 7.5
= Rs. 750000
(8) A floor is 5 m long and 4 m wide. A square carpet of side 3 m is laid on the floor. Find the area of the floor that is not carpeted.
Solution: The area of the floor = 5 m x 4 m = 20 m2
The area of square carpet = (3 m )2 = 9 m2
Therefore, The area of the floor that is not carpeted = 20 m2 – 9 m2
= 11 m2
(9) In the adjoining figure, find the area of the path which is 2 m all around.
Solution: Total area of the given figures in books = 100 m x 60 m = 6000 meter square.
Here it is given that, the path is 2 m all around.
So, here we have to find inner area, by subtracting 2 m path from total length and total breadth.
Therefore, Inner length is = (100 m – 2 – 2) = 96 m
Inner breadth is = (60 m – 2 – 2) = 56 m
Now, Inner area = 96 m x 56 m = 5376 m2
Therefore, area of the path = Total Area – Inner Area
= 6000 meter square – 5376 meter square
= 624 meter square.
(10) Four square flower beds of side 1 m 50 cm are dug on a rectangular piece of land 8 m long and 6 m 50 cm wide. What is the area of the remaining part of the land.
Solution: Here side of one flower beds = 1 m 50 cm = 150 cm
The area of four flower beds = 4 x (150)2
= 4 x 22500
= 90000 cm2
Here, the length of land = 8 m = 800 cm
Breadth of the land = 6 m 50 cm = 650 cm
The area of the land = 800 cm x 650 cm
= 520000 cm2
∴ The area of the remaining part of the land = 520000 cm2 – 90000 cm2
= 430000 cm2
= 43 m2 (divide the area value by 10000)
(11) How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to cover a rectangular region whose length and breadth are respectively:
(i) 70 cm and 36 cm (ii) 144 cm and 1 m
Solution: (i) area of the tiles = 12 cm x 5 cm = 60 cm2
Area of rectangular region = 70 cm x 36 cm
= 2520 cm2
Total tiles needed = 2520 / 60 = 42 pieces.
(ii) area of the tiles = 12 cm x 5 cm = 60 cm2
Area of rectangular region = 144 cm x 100 cm (As 1 m = 100 cm)
= 14400 cm2
Total tiles needed = 14400 / 60 = 260 pieces.
(12) The area of rectangular plot is 340 sq. m and its length is 17 m. Find the breadth of the plot and the perimeter.
Solution: The area of the rectangular plot = 340 sq m.
Length = 17 m
∴ Breadth = 340 / 12 = 20 m.
The perimeter of the field = 2 x (17 + 20)
= 2 x 37
= 74 m
(13) If the area of a rectangular plot is 144 sq. m and its length is 16 m. Find the breadth of the plot and the cost of fencing it at the rate of Rs. 6 per metre.
Solution: Here the area of the plot = 144 sq m.
Length is = 16 m.
∴ Breadth is = 144 / 16
= 9 m.
The perimeter of the rectangular plot = 2 x (16 + 9)
= 2 x 25
= 50 m
Cost needed for fencing = 50 m x 6
= Rs. 300
(14) split the following shapes into rectangles and find their areas (The measure are given in centimetres)
Solution: (1st) Area = (2 x 12) + (2 x 8) = 24 + 16 = 40 cm square.
(2nd) Area = 5 x (7 x 7) = 5 x 49 = 245 cm square.
(3rd) Area = (5 x 1) + (4 x 1) = 5 + 4 = 9 cm square.
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