Question

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?

Answer 1

Each side of the triangle = a 

Perimeter of the triangle = 3a 

∴ s = 3a / 2

Hence, area of the signal board = a² / 4 \3 sq units Ans. 

Now, perimeter = 180 cm 

Each side of the triangle = 180/ 3 cm = 60 cm 

Area of the triangle = ( 60)² / 4  × 3 cm² = 900\ 3 cm² Ans.