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If its perimeter of an equilateral triangle is 180 , what will be its area ??

Posted by S Vinay Kumar 5 years, 10 months ago

CBSE > Class 09 > Mathematics

2 answers

Dj Jd 5 years, 10 months ago

900√3 cm^2

0Thank You

Yogita Ingle 5 years, 10 months ago

{tex}Let\: side\: of \: an : equilateral \: triangle = a \: cm{/tex}

{tex}Perimeter \: of \: the \: triangle\ (P) = 180\:cm \: (given){/tex}

{tex}\implies 3a = 180\:cm{/tex}

{tex}\implies a = \frac{180}{3}{/tex}

{tex}\implies a = 60\:cm{/tex}

{tex}Area\: of \: an\ \: equilateral \: triangle (A) =\frac{\sqrt{3}}{4}\times a^{2}{/tex}

{tex}=\frac{\sqrt{3}}{4}\times 60^{2}\\=\frac{\sqrt{3}}{4}\times 60\times 60\\=\frac{\sqrt{3}}{4}\times 60\times 15\\=900\sqrt{3} \:cm^{2}{/tex}

Therefore,

{tex}Area\: of \ \: equilateral \: triangle (A)\ =900\sqrt{3}\:cm^{2}{/tex}

2Thank You

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