HMMT 2004 G7

Yet another trapezoid $A B C D$ has $A D$ parallel to $B C . A C$ and $B D$ intersect at $P$. If $[A D P] /[B C P]=1 / 2$, find $[A D P] /[A B C D]$. (Here the notation $\left[P_{1} \cdots P_{n}\right]$ denotes the area of the polygon $P_{1} \cdots P_{n}$.)