2003 AMC 12B Problem 15

Let $O$ be the center of the octagon. Joining $O$ to the vertices splits the octagon into $8$ congruent triangles, so $\triangle AOB$ has area $\dfrac{1}{8}.$ Since $O$ is the midpoint of $\overline{AE},$ triangles $AOB$ and $BOE$ have equal areas, so $\triangle ABE$ has area $\dfrac{1}{4}.$ The rectangle $ABEF$ is split by diagonal $\overline{BE}$ into two congruent triangles, so $\triangle ABE$ is half of it. Hence $ABEF$ has area $\dfrac{1}{2}.$ Thus, the correct answer is D.