Page 139 - Maths Skills - 7

Perimeter and Area 137

PQ = (3 + 40 + 3) m = 46 m and

QR = (3 + 20 + 3) m = 26 m
\ Area of the rectangle PQRS = 46 m × 26 m = 1196 m 2 3m
⇒ Area of the path = Area of PQRS – Area of ABCD

= (1196 – 800) m = 396 m 2 3 m
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Example 3: A rectangular plot is 60 m by 50 m. Two crossroads each 3 m wide
are running through the middle of the field, such that each path is
parallel to one of the sides of the rectangle. Find the total area used
as path and also find the cost of gravelling the roads at ` 4.50 per m .
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Solution: Let EFGH and ABCD be the crossroads.

Given, FG = 60 m and EF = 3 m
\ Area of the road EFGH = (60 × 3) m = 180 m 2
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Again, AD = 50 m and AB = 3 m
\ Area of the road ABCD = (50 × 3) m = 150 m .
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It is clear that the square PQRS is common to both the roads.
\ Area of the square PQRS = (3 × 3) m = 9 m 2
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Now, total area of both the crossroads = Area of road EFGH + Area of road ABCD – Area of PQRS
= (180 + 150) m – 9 m = 321 m 2
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\ Cost of gravelling the roads = ` 4.50/m × 321 m = ` 1444.50.
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Exercise 8.3

1. The length and breadth of a rectangular hall are 40 m and 32.5 m respectively. A carpet is to be laid
inside the hall leaving all around a margin of 1.5 m from the four walls of the hall. Find.
(i) the area of the carpet (ii) the area of the strip left uncovered.

2. A square lawn is surrounded by a path 2.5 m wide around it. If the area of the path is 200 sq m, find the
area of the lawn.

3. A square garden of side 55 m has a path 2 m wide inside the lawn along its boundary. Find the area of
the path. Also find the cost of planting grass in the rest of the garden at the rate of ` 8 per m .
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4. The length and breadth of a plot are in the ratio of 5 : 3 and its perimeter is 320 m. A 3 m wide path runs
along the inside boundary. Find the cost of paving the path at ` 2.5 per sq m.
5. Find the cost of paving a pathway 1.5 m wide immediately outside a flower garden 25 m × 12 m at
` 22 per m .
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6. A rectangular path is shown in Fig. 1 and 2. Find the area of the single shaded region in Fig. 1 and the
double shaded region in Fig. 2 according to the measures given.

Fig. 1 Fig. 2