1998 AIME Problem 11

Three of the edges of a cube are \overline{A B}, \overline{B C}, and \overline{C D}, and \overline{A D} is an interior diagonal. Points P, Q, and R are on \overline{A B}, \overline{B C}, and \overline{C D}, respectively, so that A P=5, P B=15, B Q=15, and C R=10. What is the area of the polygon that is the intersection of plane P Q R and the cube?