∵△DOC和△OBC在BD边上等高
∴OD/OB=S△DOC/S△OBC=6/12=1/2
∵AD∥BC
∴△AOD∽△OBC
∴S△AOD/S△OBC=(OD/OB)²=(1/2)²=1/4
即S△AOD=1/4S△OBC=1/4×12=3
∵△ABC和△BCD等高,等底
∴S△AOB=S△ABC-S△OBC=S△BCD-S△OBC=S△OBC+S△DOC-S△OBC=S△DOC=6
∴S△AOD+S△AOB=3+6=9