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”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Let a, b and c be the sides of the triangle.

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

By formula,

Semi Perimeter (s) = $\dfrac{\text{Perimeter of triangle}}{2} = \dfrac{a + b + c}{2}$

= $\dfrac{11 + 6 + 15}{2} = \dfrac{32}{2}$ = 16 m.

By Heron's formula,

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

Substituting values we get :

$A = \sqrt{16(16 - 11)(16 - 6)(16 - 15)} \\[1em] = \sqrt{16 \times 5 \times 10 \times 1} \\[1em] = \sqrt{800} \\[1em] = 20\sqrt{2} \text{ m}^2.$

Hence, area of the wall painted in colour = $20\sqrt{2}$ m².