What is the area of the shaded region?

In the diagram above, the length of a side of square ABCD is four units.

What is the area of the shaded region?
A . 4
B . 4 C π
C . 4 C 4π
D . 16π
E . 16 C 4π

Answer: B

Explanation:

The area of a square is equal to S2 , where S is the length of a side of the square. The area of ABCD is 4 2 = 16 square units. The area of a circle is equal to π r2 , where r is the radius of the circle.

The diameter of the circle is four units. The radius of the circle is 4/2 = 2 square units. The area of the circle is equal to π × 2 2 = 4π. The shaded area is equal to one-fourth of the difference between the area of the square and the area of the circle: 1/4 × (16 C 4π) = 4 C π.