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, let's go through the solution step by step.

### Step 1: Understand the properties of the equilateral triangle
An equilateral triangle has all three sides equal. If we denote the length of one side as \( a \), then the perimeter \( P \) of the triangle can be expressed as:
\[ P = a + a + a = 3a \]

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