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: Size of signal board = a
∴ Perimeter of signal board = a + a + a = 3a
⇒ 2s = 3a, s = (3/2)a
⇒ s = semiperimeter
Heron's formula:
Area of Δ = √s(s-a)(s-b)(s-c)
A = √((3/2)a)((3/2)a - a)((3/2)a - a)((3/2)a - a)
A = √((3/2)a)(a/2)(a/2)(a/2)
A = √(3/4)a⁴
⇒ A = (√3/4)a²
Perimeter = 180 cm (given)
⇒ Side = a = 180/3 = 60 cm
⇒ A = √3/4 × 60 × 60 = 900√3 cm²