Height of an equilateral triangle is 9 cm. F | vedclass

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Question

(A) The height $(h)$ of an equilateral triangle is given by the formula $h = \frac{\sqrt{3}}{2} 	imes a$,where $a$ is the side length.Given $h = 9 \

Vedclass · Accepted Answer

$27 \sqrt{3} \, cm^2$

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(A) The height $(h)$ of an equilateral triangle is given by the formula $h = \frac{\sqrt{3}}{2} 	imes a$,where $a$ is the side length.Given $h = 9 \ cm$,we have $9 = \frac{\sqrt{3}}{2} 	imes a$.Thus,$a = \frac{18}{\sqrt{3}} = 6\sqrt{3} \ cm$.The area $(A)$ of an equilateral triangle is given by $A = \frac{\sqrt{3}}{4} 	imes a^2$.Substituting the value of $a$: $A = \frac{\sqrt{3}}{4} 	imes (6\sqrt{3})^2 = \frac{\sqrt{3}}{4} 	imes (36 	imes 3) = \frac{\sqrt{3}}{4} 	imes 108 = 27\sqrt{3} \ cm^2$.

Height of an equilateral triangle is $9 \ cm$. Find its area?

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