In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 60^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $AB = 12$, then find the area of triangle $BXA$.
By the angle bisector theorem, the area of triangle BXA is 15*sqrt(2).