Question

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.

Answer 1

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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