Page 179 - Ganit Kaushal

Ex 11. What happens to the area of a rectangle if its length and breadth are doubled?
Sol. Let the area of a rectangle be A, length = L, and breadth = B.
Then, A = L × B.
Now, new length = 2L and new breadth = 2B
\ New area = 2L × 2B = 4 (L × B) = 4A = Four times the old area.

Exercise 6.4

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1. What is the perimeter of a rectangle whose area is 650 cm and breadth is 13 cm?
2. What will be the area of a rectangle if its length is doubled and its breadth is tripled?
3. What is the perimeter of a rectangular field whose length is four times its breadth and which has an
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area equal to 30,976 cm ?
4. Manish wants to cover his room, which is 3 m wide and 4 m long, with square tiles. If each square
tile has a side of half a metre, then find the number of tiles required to cover the floor of his room.
5. A wire is cut into several small pieces. Each of the small pieces is bent into a square of side 2 cm. If
the total area of the small squares is 28 sq. cm, what was the original length of the wire?
6. One side of a square plot is 300 m. Find the cost of levelling it if the rate for levelling is `0.50 per sq m.
7. The floor of a rectangular hall is to be covered with a carpet 200 cm wide. The length and breadth of
the hall are 20 m and 18 m respectively. Find the cost of the carpet at the rate of `15 per metre.
Miscellaneous Solved Examples

Ex 1. Find the perimeter of the shape in the given figure alongside. 1 cm 4 cm 0.5 cm 2.5 cm
Sol. Perimeter = (1 + 4 + 0.5 + 2.5 + 2.5 + 0.5 + 4) cm = 15 cm 4 cm
0.5 cm 2.5 cm
Ex 2. Using the Conventional Rules (C1–C4), Sol. We observe that there is 1 full square (green dot)
find the area of the shape in the given and 8 more than half squares (blue dots) and there
figure. are no half squares.
\ Total Area = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
= 9 sq units.

Ex 3. The picture shows the plan of Sharan’s 42 ft
home. Some of the measurements are given
Kitchen
and some are missing. (NCERT) (18 ft × 10 ft)
(a) Find the missing measurements. 15 ft Master Bedroom Toilet (____ ft × ____ ft) Area = ____ Area = 180 sq. ft 10 ft Area = 70 sq. ft (____ ft × ____ ft) Utility
(12 ft × 15 ft)
(b) Find out the area of his house. Area = 180 sq. ft
(c) What is the perimeter of Sharan’s house? 25 ft 5 ft 18 ft 7 ft
Prepare a comparison table showing the 12 ft
Hall
areas and perimeters of Sharan’s house and (23 ft × ____ ft) 15 ft
Chaman’s house (Given in Example 4). 10 ft Small Bedroom Area = ____ Area = ____ (____ ft × ____ ft) Entrance
(12 ft × 10 ft)
Sol. (a) Utility: (10 ft × 7 ft); Area = 70 sq. ft Area = ____
Small Bedroom: Area = 120 sq ft 23 ft

Perimeter and Area 177