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

Length of the side of equilateral triangle = a
Perimeter of the signal board = 3a = 180 cm
∴ 3a = 180 cm ⇒ a = 60 cm
Semi perimeter of the signal board (s) = 3a/2
Using heron's formula,
Area of the signal board = √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
                                       = √3a4/16
                                       = √3a2/4
                                       = √3/4 × 60 × 60 = 900√3 cm2

Answer 2

answer is here perimeter of triangle =180
side=180/3= 60
a=60
b=60
c=60
s=a+b+c/2
=180/2=90
heron,s Formula = root s (s-a) (s-b) (s-c)
root 90(90-60) (90-60) (90-60)
root 90*30*30*30
root 3*30 *30*30*30
= root 3*30 square centimeter ans ( I hope I can help you)