Question

the height of an equilateral triangle is root 6 CM then its area is

Answer 1

See the attached file

Answer 2

Answer:

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

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

Step-by-step explanation:

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

$Height (h) = \sqrt{6}\:cm \:(given)$

$\frac{\sqrt{3}{2}} a = \sqrt{6}$

$\implies a = (\sqrt{3}\times \sqrt{2})\times \frac{2}{\sqrt{3}}$

$\implies a = 2\sqrt{2}\:cm$

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

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

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

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

$= \sqrt{3} \times 2$

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

Therefore.,

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

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

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