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

We know that, 

The Heron's formula for calculating the area of the triangle,

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

where, s is the semi-perimeter = half of the perimeter

here, perimeter is 180 cm

we draw the diagram for better understanding of the question, 

we observe that,

the each side of traffic signal board = a cm

Thus,

Perimeter = a $+$ a $+$ a  = 3a

Semi- perimeter = 3a/2

here, all three sides are of equal to a cm

Hence, we get

Area of a single board = $\sqrt{s (s - a) (s - b) (s -c)}$

= $\sqrt{s (s-a) (s-a) (s-a)}$

= (s - a) $\sqrt{s (s-a)}$

s = 3a/2

Thus,

area of the single board= (3a/2 - a) $\sqrt{3a/2(3a/2 -a)}$

= $\frac{\sqrt{3}}{4}$ a²

where, a = 60 cm

Area of the single board = $\frac{\sqrt{3}}{4}$ $\times$ (60)²

= 900 $\sqrt{3}$ cm²