2003 AMC 12B Problems/Problem 15

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

$\text {(A) } 1-\frac{\sqrt{2}}{2} \qquad \text {(B) } \frac{\sqrt{2}}{4} \qquad \text {(C) } \sqrt{2}-1 \qquad \text {(D) } \frac{1}{2} \qquad \text {(E) } \frac{1+\sqrt{2}}{4}$ These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

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2003 AMC 12B Problems/Problem 15