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?
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Answer 1

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Answer 2

Given:

• A traffic signal board, indicating 'SCHOOL AHEAD', is an equilateral triangle with side 'a'
• The perimeter of the equilateral triangle is 180 cm.

To be found:

The are of the equilateral triangle signal board

As it is an equilateral triangle so, all sides of the triangle will be equal.

So,

The perimeter of the triangle = 180 cm

⇒ a + a + a = 180

⇒ 3a = 180

⇒ a = 180 ÷ 3

⇒ a = 60 cm

So, the length of each side of the triangle 60 cm.

Now,

Heron's Formula-

$= \sqrt{S(S-a)(S-b)(S-c)}$ cm sq.

[Here S = periemeter÷  2, (a, b, c) are the sides of triangles]

Now,

S = 180 ÷ 2

  = 90

And,

The sides of the triangle = a = b = c = 90 cm

So,

Area of the triangle  

$= \sqrt{90(90-60)(90-60)(90-60)}$

$= \sqrt{90(30)(30)(30)}$

$= \sqrt{3\underline{(30)(30)}\ \underline{(30)(30)}}$

= 30 × 30 √3

= 900√3 cm²

Hence,

Area the traffic signal board is  900√3 cm²