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  • Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads.

Q 6. Two cross roads, each of width $10$ m , cut at right angles through the centre of a rectangular park of length $700$ m and breadth $300$ m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

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It is given that width of each road is 10 m and the length of rectangular park is 700 m and breadth is 300 m Now, We know that the area of a rectangle is = length $\times$ breadth
The area of the total park is
$\Rightarrow 700 \times 300=210000 \mathrm{~m}^2$------(i)
The area of road parallel to the width of the park (PQRS) is
$\Rightarrow 300 \times 10=3000 \mathrm{~m}^2$--------(ii)
The area of road parallel to the length of the park (EHGF) is
$\Rightarrow 700 \times 10=7000 \mathrm{~m}^2$-------(iii)
The common area of both the roads (KMLN) is
$\Rightarrow 10 \times 10=100 \mathrm{~m}^2$-------(iv)
Area of roads $=[(ii)+(iii)-(iv)]$
$\Rightarrow 7000+3000-100=9900 \mathrm{~m}^2=0.99 h a$-----(v)
Now, the Area of the park excluding the crossroads is $=[(i)-(v)]$
$\Rightarrow 210000-9900=200100 m^2=20.01 h a$

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