Question

$△ABC$ is an equilateral triangle with side AC = 6cm. Find the area of the incircle.

• A. $6\pi$
  
• B. $3\pi$
  
• C. $\sqrt{3\pi }$
  
• D. $12\pi$

Answer 1

The correct option is B

$3\pi$

Radius of a inner circle is given by $r=a\frac{\sqrt{3}}{6}$
Therefore $r=6\times \frac{\sqrt{3}}{6}=\sqrt{3}$
Area of the circle $=\pi r^2=\pi {\surd 3}^2=3\pi$