Question

A circle is inscribed in a square of side $\sqrt{6}$. What is the area of the circle?

• A. $\frac{3}{2}\pi$
• B. 6$\pi$
• C. $\pi$
• D. 9$\pi$

Answer 1

The correct option is A $\frac{3}{2}\pi$

The inscribed circle in a square of area 6 is
The side AD = $\sqrt{6}$ and also the diameter = $\sqrt{6}$ The radius of the circle O is OF = $\frac{\sqrt{6}}{2}\Rightarrow OF=\sqrt{\frac{3}{2}}$
The area of the circle of radius $\sqrt{\frac{3}{2}}$ is
Area = $\pi {\left(\sqrt{\frac{3}{2}}\right)}^2\Rightarrow$

Area = $\frac{3}{2}\pi$