Three of the edges of a cube are $$\overline{AB}, \overline{BC},$$ and $$\overline{CD},$$ and $$\overline{AD}$$ is an interior diagonal. Points $$P, Q,$$ and $$R$$ are on $$\overline{AB}, \overline{BC},$$ and $$\overline{CD},$$ respectively, so that $$AP = 5, PB = 15, BQ = 15,$$ and $$CR = 10.$$ What is the area of the polygon that is the intersection of plane $$PQR$$ and the cube?

(第十六届AIME1998 第11题)