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?
Given:
Length of the side of the equilateral triangle = a
Perimeter of the signal board = perimeter of triangle
= 3a = 180 cm
Hence,
3a = 180cm
a = 60 cm
Semi perimeter of the signal board (s),
= 
Now,
Using Heron’s formula,
Area of the signal board = 
= 
= 
, putting a = 60
30