imc

We know $AM=\frac{10}{2}=5$ by the Pythagorean theorem, and furthermore, $△AME$ is similar to $△ABC$. Therefore, $ME=5\cdot \frac{6}{8}=\frac{15}{4}$, and the area of the triangle is $5\cdot \frac{15}{4}\cdot \frac{1}{2}=\boxed{\frac{75}{8}}$.