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

Answer 1

Answer:

Using Heron's Formula

Measure of each side of triangle = a

Perimeter of the triangle = 180 cm

a+a+a = 180 cm

3a = 180 cm

a = 180/3

a = 60 cm

Semi-Perimeter (S) = sum of all sides/2

= a+a+a/2

= 180/2

= 90cm

Area =√s(sa)(s-b)(s-c)

=√90(90-60)(90-60)(90-60)

=√90*30*30*30

=√3*3*5*2*3*5*2*3*5*2*3*5*2

=3*3*5*5*2*2*√3

=900√3 cm^2

Answer 2

Step-by-step explanation:

Given,

Side of the signal board = a

Perimeter of the signal board = 3a = 180 cm

∴ a = 60 cm

Semi perimeter of the signal board (s) = 3a/2

By using Heron’s formula,

Area of the triangular signal board will be =(in the above attached image)

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