# Q. 6.     Two cross roads, each of width $10m$, 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.

R Riya

It is given that width of each road is $10m$ and the length of rectangular park is $700\; m$ and breadth is $300\; m$

Now, We know that area of rectangle is = $length \times breadth$

Area of total park is

$\Rightarrow 700 \times 300 = 210000 \ m^2$                   -(i)

Area of road parallell to width of the park ( ABCD ) is

$\Rightarrow 300 \times 10 = 3000 \ m^2$                           -(ii)

Area of road parallel to length of park ( PQRS )  is

$\Rightarrow 700 \times 10 = 7000 \ m^2$                          -(iii)

The common area of both the roads ( KMLN ) is

$\Rightarrow 10 \times 10 = 100 \ m^2$                               -(iv)

Area of roads = $[(ii)+(iii)-(iv)]$

$\Rightarrow 7000+3000-100=9900 \ m^2 = 0.99 \ ha$                -(v)

Now, Area of the park excluding crossroads is = $[(i)-(v)]$

$\Rightarrow 210000-9900 = 200100 \ m^2 = 20.01 \ ha$

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