如图,△ABC中,DE//FG//BC,AD:DF:FB=1:2:3,则S四边形DFGE:S四边形FBCG=

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如图,△ABC中,DE//FG//BC,AD:DF:FB=1:2:3,则S四边形DFGE:S四边形FBCG=
如图,△ABC中,DE//FG//BC,AD:DF:FB=1:2:3,则S四边形DFGE:S四边形FBCG=

如图,△ABC中,DE//FG//BC,AD:DF:FB=1:2:3,则S四边形DFGE:S四边形FBCG=
面积比等于相似比的平方
DE//FG//BC,则
△ADE∽△AFD∽△ABC
S△ADE:S△AFG:S△ABC=1²:(1+2)²:(1+2+3)²=1:9:36
S△AFG=9S△ADE,S△ABC=36S△ADE
S四边形DFGE=S△AFG-S△ADE=8S△ADE
S四边形FBCG=S△ABC-S△AFG=27S△ADE
S四边形DFGE:S四边形FBCG=8:27

因为AD:AF:AB=1:3:6
所以S△ADE:S△AFG:S△ABC=1:9:36
所以S四边形DFGE:S四边形FBCG=(9-1):(36-9)=8:27