Triangle $ABC$ has $AB=BC=5$ and $AC=6$. Let $E$ be the foot of the altitude from $B$ to $\overline{AC}$ and let $D$ be the foot of the altitude from $A$ to $\overline{BC}$.  Compute the area of triangle $DEC$.
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<|im_start|>user
Triangle $ABC$ has $AB=BC=5$ and $AC=6$. Let $E$ be the foot of the altitude from $B$ to $\overline{AC}$ and let $D$ be the foot of the altitude from $A$ to $\overline{BC}$.  Compute the area of triangle $DEC$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{108}{25}
Triangle $ABC$ has $AB=BC=5$ and $AC=6$. Let $E$ be the foot of the altitude from $B$ to $\overline{AC}$ and let $D$ be the foot of the altitude from $A$ to $\overline{BC}$.  Compute the area of triangle $DEC$.
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