Question

Perimeter of an equilateral triangle is 24 cm if its height is 6 cm. Find its area?

Answer 1

/* There is a mistake in the problem . Height is not equal to 6 cm */

$Let \: side \:of \:an\: equilateral \: triangle = a\:cm$

$i) Perimeter \:of \: the \: triangle = 24 \:cm$

$\implies 3a = 24 \:cm$

$\implies a = \frac{24}{3}$

$\implies a = 8 \:cm$

$ii) \red{ Area \: of \:the \: triangle }$

$= \frac{\sqrt{3}}{4} a^{2}$

$= \frac{\sqrt{3}}{4}\times 8^{2}$

$= \frac{\sqrt{3}}{4}\times 8\times 8$

$= \sqrt{3} \times 8 \times 2$

$= 16\sqrt{3}\:cm^{2}$

Therefore.,

$\red{ Area \:of \:the \: equilateral \: triangle}$

$\green { = 16\sqrt{3}\:cm^{2} }$

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