Question

A traffic signal board indicating SCHOOL AHEAD is a equilateral triangle with side 'a' . Find the area of the signal board using herons formula . If its perimeter is 180 cm ,what will be the area of the signal board ?

Answer 1

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Answer 2

${\bold{Given}} : \: Perimeter \: of \: signal \: board \: = 180 \: cm$

$Length \: of \: the \: side \: of \: equilateral \: \triangle \: = \: a$

$Perimeter \: of \: signal \: board \: = \: perimeter \: of \: triangle$

$\because \: perimeter \: of \: euilateral \: triange \: = \: 3 \times sides$

$\implies \: 3a \: = 180 \degree$

$\implies \: a \: = \dfrac{ \cancel{180\degree}} {\cancel{3}} \: \: \: \large( \: cross \: multipied \large)$

$\implies \: a \: = \: 60 \: cm$

$\Large {Now }$

$Semi \: perimeter \: of \: the \: signal \: board \: = \dfrac{ \cancel{180}} {\cancel{2} </p><p>}$

$90 \: cm$

$\bold {\underline{ \underline{By \: using \: Heron's \: formula}}}$

$\boxed{Area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c}}$

$\implies \: Area \: of \: triangle \: = \sqrt{90(9 - 60)(90 - 6)(90 - 60)}$

$\implies \: Area \: of \: triangle \: = \sqrt{90 \times 30 \times 30 \times 30}$

$\implies \: Area \: of \: triangle \: = \sqrt{30 \times3 \times 30 \times 30 \times 30}$

$\implies \: Area \: of \: triangle \: = 30 \times 30\sqrt{3}$

$\implies \: Area \: of \: triangle \: = \large\bold { \underline { \underline{900\sqrt{3}}}}$