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

$\huge \underline\textbf{AnsWer}$

Let 2s be the perimeter of of the signal board. Then,

$\blue{\bold{2s\:a\:+\:a\:+\:a}}$

$\blue{\bold{s\:=\: \frac{3a}{2}}}$

Let △ be the area of the given equilateral triangle. Then,

△ = $\blue{\bold{ \sqrt{s(s-a)(s-b)(s-c)}}}$

△ = $\blue{\bold{ \sqrt{ \frac{3a}{2}\:( \frac{3a}{2}\:-\:a )\:(\frac{3a}{2}\:-\:a )\:(\frac{3a}{2}\:-\:a )}}}$

△ = $\blue{\bold{ \sqrt{ \frac{3a}{2}\:×\: \frac{a}{2}\:×\: \frac{a}{2}\:×\: \frac{a}{2}}}}$ = $\blue{\bold{ \sqrt{ \frac{ {3a}^{4}}{16}}}}$ = $\blue{\bold{ \frac{ \sqrt{3}}{4}}}$ $\blue{\bold{ {a}^{2}}}$

if perimeter = 108 cm Then,

2s = 108

3a = 108

a = 60

△ = $\blue{\bold{ \frac{ \sqrt{3}}{4}\:×\:( {60})^{2}}}$

=$\sf\huge\underline\green {\sqrt[900]{3}}$ $\sf\huge\underline\green{{cm}^{2}}$

Answer 2

Given,

Side of the signal board = a

Perimeter of the signal board = 3a = 180 cm

∴ a = 60 cm

Semi perimeter of the signal board (s) = 3a/2

By using Heron’s formula,

Area of the triangular signal board will be =(in the above attachment)

$\huge \mid {\colorbox {cyan} {@vanunagar13❤~}}\mid$