2012 xIMC keystage2-EMIC individual Question 14

In square $ABCD$, $M,N$ are midpoints of $AB,BC$. On $CD$, $CP=4$, $PD=8$ cm; on $DA$, $DQ=3$ cm. Lines $MP,NQ$ meet at $O$. Find the largest absolute area difference among pairs $(QOM,QAM),(MON,MBN),(NOP,NCP),(POQ,PDQ)$.