XXI OBM

Let $AD$ meet $EC$ and $EB$ at $R$ and $S$ respectively. $PQDR$ is a parallelogram, so the area of $PQD$ equals the area of $RQD$, which by its turn equals the area of $ERS$. Therefore the area of $APQD$ equals the area of $APDRES$, which is half of the area of the whole star.