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There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 12.10 ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Q3.    There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 12.10 ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

            

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Given the sides of the triangle are:

a = 15 m,\ b= 11m\ and\ c= 6m.

So, the semi perimeter of the triangle will be:

s = \frac{a+b+c}{2} = \frac{15+11+6}{2} = \frac{32}{2} = 16m

Therefore, Heron's formula will be:

A = \sqrt{s(s-a)(s-b)(s-c)}

     = \sqrt{16(16-15)(16-11)(16-6)}

     = \sqrt{16(1)(5)(10)}

    = \sqrt{(4\times 4)(1)(5)(5\times 2 )}

    = 4\times 5 \sqrt2 = 20\sqrt2\ m^2

Hence, the area painted in colour is 20\sqrt2\ m^2.

 

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