2003 AMC 10B 第 23 题

Let $O$ be the center of the octagon, where the diagonals of $ABEF$ meet

Triangle $AOB$ is one of the eight congruent triangles making up the octagon

Let $O$ be the center. The octagon splits into $8$ congruent triangles from $O,$ so $\triangle AOB$ has area $\dfrac18.$

Since $O$ is the midpoint of $AE,$ triangles $AOB$ and $BOE$ have equal area, so $\triangle ABE$ has area $\dfrac14.$ The rectangle $ABEF$ is twice this, namely $\dfrac12.$

Thus, the correct answer is D.