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# An equilateral triangle is inscribed in a circle with a radius of 2 meters. What is the area of this triangle?

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#### Explanation

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Jun 5, 2017

Area $= 3 \sqrt{3} {\text{ m}}^{2}$

#### Explanation:

As shown in the figure, $\Delta A B C$ is an equilateral triangle inscribed in a circle centered at $O$
Given radius $r = 2 m$,
$\implies O M = h = r \sin 30 = 2 \times \frac{1}{2} = 1$
$B M = \frac{a}{2} = r \cos 30 = 2 \times \frac{\sqrt{3}}{2} = \sqrt{3}$
$A M = r + h = 2 + 1 = 3$
As $A M$ bisects $B C , \implies B C = 2 B M = a = 2 \sqrt{3}$
Area of $\Delta A B C = \frac{1}{2} \times A M \times B C = \frac{1}{2} \times 3 \times 2 \sqrt{3} = 3 \sqrt{3} {\text{ m}}^{2}$

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