Question

A tramc 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:

$30\sqrt{3}cm^2$

Step-by-step explanation:

Given,

side of equilateral triangle= a

perimeter of triangle =180 cm

semi-perimeter of triangle,s = $\frac{perimeter}{2}$

                                           s=$\frac{180}{2}$

                                           s=90 cm

since the perimter of equilateral traingle=$3\times side od triangle$

                      180=3a

                    a=60 cm

According of Heron's formula ,

area of traingle with side a and semi-perimeter s =$\sqrt{s(s-a)(s-b)(s-c)} \\=\sqrt{90(90-60)(90-60)(90-60)}\\=\sqrt{90(30)(30)(30)} \\=30\sqrt{3} cm^2$