Question : If the height of the equilateral triangle is $2 \sqrt 3\:\operatorname{cm}$, then determine the area of the equilateral triangle.
Option 1: $6\:\operatorname{cm^2}$
Option 2: $2\sqrt3\:\operatorname{cm^2}$
Option 3: $4\sqrt3\:\operatorname{cm^2}$
Option 4: $12\:\operatorname{cm^2}$

Question

Question : If the height of the equilateral triangle is $2 \sqrt 3\:\operatorname{cm}$, then determine the area of the equilateral triangle.

Option 1: $6\:\operatorname{cm^2}$

Option 2: $2\sqrt3\:\operatorname{cm^2}$

Option 3: $4\sqrt3\:\operatorname{cm^2}$

Option 4: $12\:\operatorname{cm^2}$

Team Careers360 · Accepted Answer

Correct Answer: $4\sqrt3\:\operatorname{cm^2}$

Solution : In an equilateral triangle, the height $(h)$ is related to the side length $(a)$,
$h = \frac{\sqrt{3}}{2}a$
Given that the height of the equilateral triangle is $2\sqrt{3}\: ext{cm}$.
⇒ $2\sqrt{3} = \frac{\sqrt{3}}{2}a$
⇒ $a = \frac{2\sqrt{3} imes 2}{\sqrt{3}} = 4\: ext{cm}$
The area $(A)$ of an equilateral triangle,
$A = \frac{\sqrt{3}}{4}a^{2}= \frac{\sqrt{3}}{4}(4)^{2} = 4\sqrt{3}\: ext{cm}^{2}$
Hence, the correct answer is $4\sqrt{3}\: ext{cm}^{2}$.

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Question : If the height of the equilateral triangle is $2 \sqrt{3} cm$ , then determine the area of the equilateral triangle.
Option 1: $6 {cm}^{2}$
Option 2: $2 \sqrt{3} {cm}^{2}$
Option 3: $4 \sqrt{3} {cm}^{2}$
Option 4: $12 {cm}^{2}$