Question 56
In a rectangular box $A B C D E F G H$ with edge lengths $A B = A D = 6$ and $A E = 49$, a plane slices through point $A$ and intersects edges $B F$, $F G$, $G H$, $H D$ at points $P$, $Q$, $R$, $S$ respectively. Given that $A P = A S$ and $P Q = Q R = R S$, find the area of pentagon $A P Q R S$.