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?

Options

A. ` 900 sqrt(3) cm^(2)`
B. ` 800 sqrt(3) cm^(2)`
C. ` 950 sqrt(3) cm^(2)`
D. ` 400 sqrt(3) cm^(2)`

Answer

A

Explanation

We know that, an equilateral triangle has equal sides. So, all sides are equal to a.
Perimeter of triangle = 180 cm `" "` (given)
`rArr a+a+a=180`
`rArr 3a=180`
`rArr a=60 cm`
`s=(a+a+a)/(2)=(180)/(2) " " (.:. 2s = a+b+c)`
`s=90 cm`
Area of equilateral triangle = `sqrt(s(s-a)(s-a)(s-a)) " " `[`:'` Heron's formula, `s=sqrt(s(s-a)(s-b)(s-c))`]
`=sqrt(90(90-60)(90-60)(90-60))`
`=sqrt(30xx3xx30xx30xx30)=30xx30 sqrt(3)`
`= 900 sqrt(3) cm^(2)`