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 below). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
Solution and Explanation
By, Heron's formula
Area = \(\sqrt{\text{s(s - a)(s - b)(s - c)}}\)
The sides of the triangular walls are a = 11 m, b = 6 m and c = 15 m.
Semi Perimeter:
\(s =\)\( \frac{\text{(a + b + c)}}{2}\)
\(= \frac{\text{(11 + 6 + 15)}}{2}\)
\(= \frac{32}{2}\)
= 16 m
By using Heron’s formula,
Area of triangular wall = \(\sqrt{\text{s(s - a)(s - b)(s - c)}}\)
Substituting the given values in formula,
\(= \sqrt{\text{16(16 -11)(16 - 6)(16 -15)}}\)
\(= \sqrt{\text{16 × 5 × 10 × 1}}\)
\(= \)\(\sqrt{800}\) m²
\(= 20\sqrt2\) m²
Area of the wall of the park to be painted in colour \(= 20\sqrt2\) m2.
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