How do I find the area of a circle inside a square?

Question

In the figure above, the circle with center $O$ is inscribed in square $ABCD$. What is the area of the shaded portion of the circle?

(A) $\pi/4$

(B) $\pi/2$

(C) $\pi$

(D) $3\pi/2$

(E) $2\pi$

Answer 1

Hint:
Radius of the circle is ...
Area of the whole disc is equal ...
What part of the disc is shaded?
Therefore, area of the shaded part is equal ...

Answer 2

Hint: The circle has radius $1$. By symmetry (join the centre of the circle to the other corners of the square) the shaded part of the circle is one-quarter of the whole circle.