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 18o cm what will be the area of the signal board

Answer 1

Given :-

ABC is an equilateral triangle

Therefore, a = b = c

To Find :-

Area of Triangle

Solution :-

Semi perimeter = perimeter / 2

s = 180 / 2

s = a + a + a /2 [ Since in equilateral triangle all the sides are equal ]

s = 3a/2

Area of signal boards = √s (s - a)(s - b)(s - c)

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

= √ 3a/2 × a/2 × a/2 × a/2

= √3a^4/2^4

= √3 a^2/2^2--(1)

= √3a^2/4

Perimeter = 180 cm

a + a + a = 180

3a = 180

a = 180/3

a = 60 cm

Substituting a = 60 in equation (1)

We get,

Area of signal boards = √3 × 60^2/4

Area of signal boards = √3 × 3600/ 4

= 900√3 cm^2

Therefore, the area of signal boards is 900√3 cm^2.