Question

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side $\text{'}a\text{'}$. Find the area of the signal board, using Heron’s formula. If its perimeter is $180cm$ what will be the area of the signal board?

Answer 1

Step 1. Find the side.

Sides of the signal board $=a$

Perimeter of the signal board $=180cm$

$$\begin{gathered} \Rightarrow a+a+a=180 \\ \Rightarrow 3a=180 \\ \Rightarrow a=60cm \end{gathered}$$

Step 2. Find the semi perimeter.

Semi perimeter of the signal board $\left(s\right)=\frac{sumofsides}{2}$

$$\begin{gathered} \left(s\right)=\frac{180}{2} \\ \left(s\right)=90cm \end{gathered}$$

Step 3. Find the area.

Using Heron’s formula, area of triangle$=\sqrt{s(s-a)(s-b)(s-c)}$

Area of the triangular signal board will be $=\sqrt{90(90-60)(90-60)(90-60)}$

$$\begin{gathered} =\sqrt{90x30x30x30} \\ =30x30\sqrt{3} \\ =900\sqrt{3}c{m}^2 \end{gathered}$$

Hence, the area of the signal board is $900\sqrt{3}c{m}^2$.