In triangle $XYZ$, $\angle X = 60^\circ$ and $\angle Y = 45^\circ$. Point $D$ lies on $\overline{YZ}$ such that $\overline{DX}$ bisects $\angle ZXY.$ If $XD = 24,$ then find the area of triangle $XYZ$.
The "successful" region has half the size of the whole triangle, so by similar triangles, the probability that the area of triangle XYD is at most 12 is 1/4.
