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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?

Q1.    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?

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Given the perimeter of an equilateral triangle is 180cm.

So, 3a = 180\ cm  or  a = 60\ cm.

Hence, the length of the side is 60cm.

Now, 

Calculating the area of the signal board by the Heron's Formula:

A = \sqrt{s(s-a)(s-b)(s-c)}

Where, s is the half-perimeter of the triangle and a, b and c are the sides of the triangle.

Therefore,

s = \frac{1}{2}Perimeter = \frac{1}{2}180cm = 90cm

a =b=c = 60cm  as it is an equilateral triangle.

Substituting the values in the Heron's formula, we obtain

\implies A = \sqrt{90(90-60)(90-60)(90-60)} = 900\sqrt{3}\ cm^2.

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