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

The given figure formed a triangle whose sides are:
a = 15m,b = 11m, c = 6m

\(s = \frac{15 + 11 + 6}{2}\)
(Since, 2s = a + b + c)

\(\Rightarrow \) \(s = \frac{32}{2}\)
\(\Rightarrow \) s = 16m

Therefore, area painted in colour
= \(\sqrt{16(16 - 15)(16 - 11)(16 - 6)}\)
(Since, Heron's formula [area = \(\sqrt{s(s - a)(s - b)(s - c)}\)])

\(\therefore \) Area
= \(\sqrt{16 × 1 × 5 × 10}\)
= \(\sqrt{2 × 2 × 2 × 2 × 5 × 5 × 2}\)
= \(\sqrt{400 × 2} {m}^2\)
\(\therefore \) the area painted in colour is \(20\sqrt{2} m^2\))