Let line $AC$ be perpendicular to line $CE$. Connect $A$ to $D$, the midpoint of $CE$, and connect $E$ to $B$, the midpoint of $AC$. If $AD$ and $EB$ intersect at point $F$, and $\overline{BC} = \overline{CD} = 15$ inches, then find the area of triangle $DFE$ in square inches.

Let's think step by step and output the final answer within \boxed{}.
user