Question

A traffic signal board, representing 'SCHOOL AHEAD', is an equilateral triangle with sides
Obtain the area of the signal board, by using Heron's formula. If its perimeter is 180 cm, what
will be the area of the signal board?​

Answer 1

Correct Question :

A traffic signal board, representing 'SCHOOL AHEAD', is an equilateral triangle with sides 'a' .Obtain the area of the signal board, by using Heron's formula. If its perimeter is 180 cm, what will be the area of the signal board?

Given :

• A traffic signal board which is an equilateral traingle with sides a.
• Perimeter = 180cm

To Find :

• Area of Signal Board.

Solution :

$\longmapsto\tt{Let\:its\:three\:sides\:be=a}$

$\longmapsto\tt{Perimeter=180cm}$

$\longmapsto\tt{a+a+a=180}$

$\longmapsto\tt{3a=180}$

$\longmapsto\tt{a=\cancel\dfrac{180}{3}}$

$\longmapsto\tt\bf{a=60}$

So , The sides of Traingle are 60cm each..

Now ,

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{60+60+60}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{180}{2}}$

$\longmapsto\tt\bf{s=90cm}$

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{90(90-60)(90-60)(90-60)}}$

$\longmapsto\tt{\sqrt{90\times{30}\times{30}\times{30}}}$

$\longmapsto\tt{\sqrt{3\times{3}\times{2}\times{5}\times{2}\times{3}\times{5}\times{2}\times{3}\times{5}\times{2}\times{3}\times{5}}}$

$\longmapsto\tt{3\times{2}{5}{3}{2}{5}\sqrt{3}}$

$\longmapsto\tt\bf{900\sqrt{3}{cm}^{2}}$

So , The Area of Signal Board is 900√3 cm²..