Question 11
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?