2003 AMC 12B Problem 15

A regular octagon ABCDEFGH has an area of one square unit. What is the area of the rectangle ABEF?

\text {(A) } 1-\frac{\sqrt{2}}{2} \qquad \text {(B) } \frac{\sqrt{2}}{4} \qquad \text {(C) } \sqrt{2}-1 \qquad \text {(D) } \frac{1}{2} \qquad \text {(E) } \frac{1+\sqrt{2}}{4}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.