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)