AMC 12 2003b Problem 15

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

File:Problem_15.PNG

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