Question

Find the area of equilateral triangle inscribed in a circle of unit radius.

• A. 3/4
• B. $\frac{3\sqrt{3}}{4}$
• C. 3
• D. $\frac{3\sqrt{3}}{2}$

Answer 1

The correct option is B $\frac{3\sqrt{3}}{4}$

The radius of circumcircle of equilateral triangle is $\frac{2}{3}h=1h=\frac{3}{2}$

The side of equilateral triangle is given as $\frac{4h}{\sqrt{3}}\frac{4}{\sqrt{3}}\times \frac{3}{2}=2\sqrt{3}$

The area of triangle is given as $\frac{\sqrt{3}}{4}(2\sqrt{3}{)}^2=3\sqrt{3}$