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There is a slide in the park. One of its side walls has been painted in the same colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

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#### Solution

It can be observed that the area to be painted in colour is a triangle, having its sides as 11 m, 6 m, and 15 m.

Perimeter of such a triangle = (11 + 6 + 15) m

2 *s* = 32 m

*s* = 16 m

By Heron’s formula,

`"Area of Triangle "=sqrt(s(s-a)(s-b)(s-c))`

`= [sqrt(16(16-11)(16-6)(16-15))]m^2`

`=(sqrt(16xx5xx10xx1))m^2`

`=20sqrt2m^2`

`"Therefore, the area painted in colour is "20sqrt2m^2`

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