jmc

Let $[ABC]$ denote the area of figure $ABC$. Clearly, $[BEDC]=[ABCD]-[ABE]$. Using basic area formulas, $[ABCD]=(BC)(BE)=80$ $[ABE]=(BE)(AE)/2=4(AE)$ Since $AE+ED=BC=10$ and $ED=6$, $AE=4$ and the area of $△ABE$ is $4(4)=16$. Finally, we have $[BEDC]=80-16=64\to \boxed{64}$