∵AD/DF=1/2
∴AD/AF=1/3
∵DE∥FG
∴S△ADE/S△AFG=（AD/AF）²=（1/3）²
S△ADE=1/9S△AFG
∵BF=3/6AB=1/2AB
∴AF/AB=1/2
∴S△AFG/S△ABC=(AF/AB)²=(1/2)²=1/4
S△AFG=1/4S△ABC
∴S△ADE=1/9×1/4S△ABC=1/36S△ABC
∴S四边形DEGF=S△AFG-S△ADE=(1/4-1/36)S△ABC=8/36S△ABC
S四边形FBCG=S△ABC-S△AFG=(1-1/4)S△ABC=3/4S△ABC=27/36S△ABC
∴S四边形DEGF∶S四边形FBCG=(8/36S△ABC)∶(27/36S△ABC)=8∶27