# 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

Side of the signal board = a

Perimeter of the signal board = 3a = 180 cm

∴ a = 60 cm

Find out

We have to determine the Area of the triangular signal board

Semi perimeter of the signal board (s) = 3a/2

Formula

By using Heron’s formula, are of triangle= $$\sqrt{s(s-a)(s-b)(s-c)}$$

Solution

Area of the triangular signal board will be =

= √90(90-60)(90-60)(90-60)

= √90×(30)×(30)×(30)

= 900√3 cm2

Hence, the area of the signal board = 900√3 cm2