Isosceles Triangle Spanning a Rectangle

As shown in the figure, in rectangle $ABCD$ the points $E$ and $F$ lie on sides $AB$ and $BC$ respectively. Triangle $DEF$ is isosceles with base $DE$, and its altitude $FG$ to the base satisfies $FG = DE$. If $\triangle ADE$ and $\triangle CDF$ each have area $20$, find the area of $\triangle BEF$.