# A circle has a radius of 6 inches. What would be the area of an inscribed equilateral triangle?

Dec 6, 2015

Area = 27$\sqrt{3}$

#### Explanation:

Length of a side of an equilateral triangle inscribed in a circle = $r \sqrt{3}$ , where r is the radius of the circle

Therefore, Area = $\sqrt{3} {a}^{2} / 4$
$a = 6 \sqrt{3}$

Note: how to get the above relation?

$\frac{a}{\sin} A = \frac{c}{\sin} C$

$\implies c = a \cdot \left(\sin \frac{C}{\sin} A\right) = 6 \cdot \left(\sin \frac{120}{\sin} 30\right) = 6 \sqrt{3}$