SMO 2008 Senior Round 1 Question 29

The figure shows triangle $ABC$ with $AB=AC$. Points $D,E$ lie on sides $AB,AC$, respectively, such that $AB=4DB$ and $AC=4AE$. If quadrilateral $BCED$ has area $52\text{ cm}^2$ and triangle $ADE$ has area $x\text{ cm}^2$, find $x$.