Question 30
Side $\overline{AB}$ of $\triangle ABC$ is the diameter of a semicircle, as shown below. If $AB=3+\sqrt{3}$, $BC=3\sqrt{2}$, and $AC=2\sqrt{3}$, then the area of the shaded region can be written as $\frac{a+(b+c\sqrt{d})\pi}{e}$, where $a, b, c, d, e$ are integers, $e$ is positive, $d$ is square-free, and $\operatorname{gcd}(a, b, c, e)=1$. Find $10000a+1000b+100c+10d+e$.
