Question

A traffic signal board, indicating 'SCHOOL AHEAD', is an equilateral triangle with side ${}^{\prime }{a}^{\prime }$. 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

Given, Perimeter $=180cm$

Semi-perimeter, $S=\frac{180}{2}$

$S=90cm$

Since all sides of an equilateral triangle are equal

So, Perimeter $=180$

$a+a+a=180$

$3a=180$

$a=60cm$

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

$=\sqrt{90(90-60)(90-60)(90-60)}$

$=\sqrt{90\times 30\times 30\times 30}$

$=\sqrt{(9\times 3\times 3\times 3)\times (10{)}^4}$

$=\sqrt{\left(9^2\right)\times 3\times (10{)}^4}$

$=9\times (10{)}^2\times \sqrt{3}$

$=9\times 100\times \sqrt{3}$

$=900\sqrt{3}c{m}^2$