Question

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

Answer 1

Since, the shape of painted colour is a triangle.

Let us assume the sides of the triangle are,

$a=15m$, $b=11m$ and $c=6m$

$\Rightarrow$$P=15m+11m+6m=32m$

$\Rightarrow$ Semi perimeter $=s=\frac{32}{2}m=16m$

Now, lets evaluate the area of triangle by using Heron's formula,

$\Rightarrow$ $A=\sqrt{s(s-a)(s-b)(s-c)}$ (Heron's formula)

$\Rightarrow$$A=\sqrt{16(16-15)(16-11)(16-6)}$

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

$\Rightarrow A=\sqrt{800}$

$\Rightarrow A=20\sqrt{2}$

Therefore, the area of the painted colour is $20\sqrt{2}{m}^2$.