Page 238 - Start Up Mathematics_7

Example 7: A door of length 2 m and breadth 1 m and a square window of dimension 0.3 m is
fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m (see figure).
Find the cost of whitewashing the wall, at the rate of ` 20 per sq. m.

Solution: Length (l) of the wall = 4.5 m
Breadth (b) of the wall = 3.6 m 1 0.3
Area of the wall = l × b = 4.5 × 3.6 = 16.20 m 2 2 3.6 m
2
Area of the door = l × b = 2 × 1 = 2 m
2
Area of the window = (side) = 0.3 × 0.3 = 0.09 m 2 4.5 m
∴ area to be whitewashed = Area of wall – (Area of door + Area of window)

= 16.2 – (2 + 0.09) = 14.11 m 2
Rate of whitewashing = ` 20 per m 2
∴ cost of whitewashing = 14.11 × 20 = ` 282.20

EXERCISE 14.1

1. Find the perimeter and area of the following rectangles:
(a) length = 12 cm, breadth = 8 cm (b) length = 20 m, breadth = 15 m
2. Find the area of the squares whose: (a) side = 8 cm (b) diagonal = 5.2 cm

3. Find the expenditure of putting a barbed wire around a 4 hectare square field, if it costs
` 45 per metre.
2
4. The area of a rectangular sheet of aluminium is 400 cm . If the breadth of the sheet is
16 cm, find its length. Also find the perimeter of the aluminium sheet.
5. A conference hall is 14 m long, 8 m wide and 4 m high. There are four windows and one
door in it. The door measures 1 m by 2 m and each window measures 1 m by 1.5 m.
(a) How many litres are needed to paint all the walls of the hall if one litre is enough for
2
covering 18 m ?
(b) What will be the cost of painting the hall if 1 litre costs ` 225?
6. Calculate the perimeter and area of each of the following figures:

8 cm

10 cm
3 cm 12 cm
(a) (b)
4 cm
7 cm
12 cm
6 cm

2 cm 3 cm
11 cm
7. A playground is 38 m 50 cm long and 61 m 50 cm wide. Find:

(a) the cost of levelling it at ` 40 per m 2

(b) the number of rounds along the boundary one should take to run 2 km

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