jmc

Since $ABC$ is a 30-60-90 triangle, we have $AB=AC\sqrt{3}=6\sqrt{3}$, and $$[ABC]=\frac{(AB)(AC)}{2}=\frac{(6)(6\sqrt{3})}{2}=\frac{36\sqrt{3}}{2}=\boxed{18\sqrt{3}}.$$