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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 180cm what will be the area of the signal board?


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Solution

Step 1. Find the side.

Sides of the signal board =a

Perimeter of the signal board =180cm

a+a+a=1803a=180a=60cm

Step 2. Find the semi perimeter.

Semi perimeter of the signal board (s)=sumofsides2

(s)=1802(s)=90cm

Step 3. Find the area.

Using Heron’s formula, area of triangle=s(s-a)(s-b)(s-c)

Area of the triangular signal board will be =90(90-60)(90-60)(90-60)

=90x30x30x30=30x303=9003cm2

Hence, the area of the signal board is 9003cm2.


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