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?

Explanation

To find the area of the equilateral triangle traffic signal board using Heron's formula, follow these steps:

### Step 1: Understand the properties of the equilateral triangle
In an equilateral triangle, all three sides are equal. Let the length of each side be \( a \).

### Step 2: Find the perimeter
The perimeter \( P \) of the triangle is given as \( 180 \, \text{cm} \). Since it is an equilateral triangle:
\[
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