There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEPTHE 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.

We know that, 

The Heron's formula for calculating the area of the triangle,

Area of triangle = $\sqrt{s (s - a) (s - b) (s -c)}$

where, s is the semi-perimeter = half of the perimeter

and  a, b and c are the sides of the triangle 

Triangular sides of walls are, a = 11 m, b = 6m, c = 15 m

Thus, Semi-perimeter 

s = (a $+$ b $+$ c)/2

= (11 $+$ 6 $+$ 15)/2

= 32/2

= 16 m

Area of a triangular wall = $\sqrt{16(16 -11)(16 - 6)(16 -15)}$

= $\sqrt{16 \times 5 \times 10 \times 1}$

= $\sqrt{800}$

= 20$\sqrt{2}$  m²

Hence, Area of the wall of the park to be painted in colour = 20$\sqrt{2}$m².