15. Around a $10 \sqrt{2}$ meters $\times 10$ meters rectangular building, there is a large, lush grassland. At a point $5 \sqrt{2}$ meters in front of the midpoint of the longer wall of the building, a wooden stake is driven into the ground. A 20-meter-long rope is then used to tie a goat to the stake. The area of the grassland that the goat can reach (in square meters) is ( ).
(A) $162.5 \pi+25$
(B) $250 \pi+25$
(C) $300 \pi+50$
(D) $325 \pi+50$
(E) None of the above answers are correct
15. (D) Let $A B C D$ be a building, and the stake $P$ is located outside the long side $A B$. Extend $P A$ to $E$ and $P B$ to $F$, it is easy to see that $A E=10=$ $B F$. The area where the goat can eat grass includes: (1) $\triangle P A B$. (2) A quarter circle with $P$ as the center, between the radii (length 20) $P E, P F$. (3) An eighth circle with $A$ as the center, between the radii (length 10) $A D, A E$. (4) An eighth circle with $B$ as the center, between the radii (length 10) $B C, B F$. Therefore, the total area is $50+300 \pi+\frac{25 \pi}{2}+\frac{25 \pi}{2}$.