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?

Open in App
Solution

## Step 1. Find the side.Sides of the signal board $=a$Perimeter of the signal board $=180cm$ $⇒a+a+a=180\phantom{\rule{0ex}{0ex}}⇒3a=180\phantom{\rule{0ex}{0ex}}⇒a=60cm$Step 2. Find the semi perimeter.Semi perimeter of the signal board $\left(s\right)=\frac{sumofsides}{2}$ $\left(s\right)=\frac{180}{2}\phantom{\rule{0ex}{0ex}}\left(s\right)=90cm$Step 3. Find the area.Using Heron’s formula, area of triangle$=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ Area of the triangular signal board will be $=\sqrt{90\left(90-60\right)\left(90-60\right)\left(90-60\right)}$ $=\sqrt{90x30x30x30}\phantom{\rule{0ex}{0ex}}=30x30\sqrt{3}\phantom{\rule{0ex}{0ex}}=900\sqrt{3}c{m}^{2}$Hence, the area of the signal board is $900\sqrt{3}c{m}^{2}$.

Suggest Corrections
19