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

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 it's perimeter is 180cm ,what will be the area of the signal board?

Answer =>

Given : A signal board that is in the shape of equilateral triangle.

We know that All sides of equilateral triangle are equals.

Therefore , a = b = c = a

Heron's Formula =>√s(s - a) (s - b) (s - c)

Now area of Triangle by using Heron's formula

Where , s = perimeter = a + b + c = 3a

2 2 2

Now, area of Triangle √3a (3a - a) (3a - a) (3a - a)

2 2. 1 2 1 2 1

=>√3a /2 (3a - 2a/2) (3a -2a/2) (3a - 2a/2)

=>√3a/2 × a/2×a/2×a/2

=>a×a √3 = √3a² _______(1)

2×2 4

Given perimeter=180cm

AB+BC+AC =180 cm

a+a+a=180cm

3a =180cm

a = 180/3

a = 60cm

Putting a=60 in equation (1)

Area of ∆ABC

=√3/4(60)²

=√3/4×60×60

=√3×900

=900√3cm²

Hence, The area of the signal board is 900√3cm²