Question #N316
A square with side length $s$ is inscribed in a circle. What is the area of the circle in terms of $s$?
A. $\pi s^2$
B. $\frac{1}{2}\pi s^2$
C. $\frac{1}{4}\pi s^2$
D. $\pi s$
Correct Answer is: A
The diagonal of the square is also the diameter of the circle. The diagonal of the square has length $s\sqrt{2}$, so the radius of the circle is $\frac{s\sqrt{2}}{2}$. The area of the circle is $\pi r^2 = \pi(\frac{s\sqrt{2}}{2})^2 = \pi s^2$.