Question 105
Given triangle $ABC$, let $D$ be a point on side $AB$ and $E$ be a point on side $AC$. Let $F$ be the intersection of $BE$ and $CD$. If $\triangle DBF$ has an area of $4$, $\triangle BFC$ has an area of $6$, and $\triangle FCE$ has an area of $5$, find the area of quadrilateral $ADFE$.