In isosceles trapezoid $ABCD$, shown here, $AB = 4$ units and $CD = 10$ units. Points $E$ and $F$ are on $\overline{CD}$ with $\overline{BE}$ parallel to $\overline{AD}$ and $\overline{AF}$ parallel to $\overline{BC}$. $\overline{AF}$ and $\overline{BE}$ intersect at point $G$. What is the ratio of the area of triangle $EFG$ to the area of trapezoid $ABCD$? Express your answer as a common fraction.