Question

An equilateral triangle with area $16\sqrt{3}$cm${}^2$ is inscribed in a circle. What is the area of the circle?

• A. 88π/3 cm²
• B. 64π/3 cm²
• C. 128π/3 cm²
• D. 180 cm²
• E. None of these

Answer 1

The correct option is B

64π/3 cm²

$\begin{array}{c}Area=\frac{\sqrt{3}}{4}{a}^2=16\sqrt{3}\left(given\right)\\ a=8\end{array}$

Radius of circumcircle of an equilateral triangle = $\frac{a}{\surd 3}=\frac{8}{\surd 3}$
$\therefore$Area of circle = $\frac{64\pi }{3}$