MathNet 2020 — Math Olympiad Vault — Part 01 Question 8

In the isosceles triangle $ABC$, let $D$ and $E$ lie on sides $AB$ and $AC$ respectively, with lines $BE$ and $CD$ meeting at $F$. Moreover, triangles $AEB$ and $ADC$ are congruent, with $AD=AE=10$ and $AB=AC=30$.
Calculate $\frac{\text{area}(ADFE)}{\text{area}(ABC)}$.