Question 76
Let $ABCD$ be a square of side length $5$, and let $E$ be the midpoint of side $AB$. Let $P$ and $Q$ be the feet of perpendiculars from $B$ and $D$ to $CE$, respectively, and let $R$ be the foot of the perpendicular from $A$ to $DQ$. The segments $CE$, $BP$, $DQ$, and $AR$ partition $ABCD$ into five regions. What is the median of the areas of these five regions?