In the figure below, $D$ is the middle point of line $\overline{AB}$, $E$ is the middle point of $\overline{BC}$. $\overline{AE}$ and $\overline{CD}$ intersect at $F$. What is the area ratio $\triangle DEF$ and $\triangle ABC$?

In the figure below, $D$ is the middle point of line $\overline{AB}$, $E$ is the middle point of $\overline{BC}$. $\overline{AE}$ and $\overline{CD}$ intersect at $F$. What is the area ratio $\triangle DEF$ and $\triangle ABC$?
