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2019-02-15 · 知道合伙人教育行家
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∵S△ABE = SAECF = S△AFD
∴ S△ABE = S△AED = SABCD/3
∴AB*BE/2 = AD*DF/2 = AB*AD/3
由AB*BE/2 = AB*AD/3 得:
BE/2 = AD/3
BE = (2/3) AD
由 AD*DF/2 = AB*AD/3 得:
DF/2 = AB/3
DF = (2/3)AB
∴EC = BC-BE = AD-BE = AD-(2/3) AD = (1/3) AD
FC = CD-DF = AB-DF = AB-(2/3)AB = (1/3)AB
∴ S△CFE = 1/2*FC*EC = (1/3)AB * (1/3) AD = (1/9)AB *AD = (1/9)SABCD
∴S△AEF = SAECF-S△CFE = (1/3)SABCD-(1/9)SABCD = (2/9)SABCD
= (2/9)*AB*AD
=2/9*6*9
=12
∴ S△ABE = S△AED = SABCD/3
∴AB*BE/2 = AD*DF/2 = AB*AD/3
由AB*BE/2 = AB*AD/3 得:
BE/2 = AD/3
BE = (2/3) AD
由 AD*DF/2 = AB*AD/3 得:
DF/2 = AB/3
DF = (2/3)AB
∴EC = BC-BE = AD-BE = AD-(2/3) AD = (1/3) AD
FC = CD-DF = AB-DF = AB-(2/3)AB = (1/3)AB
∴ S△CFE = 1/2*FC*EC = (1/3)AB * (1/3) AD = (1/9)AB *AD = (1/9)SABCD
∴S△AEF = SAECF-S△CFE = (1/3)SABCD-(1/9)SABCD = (2/9)SABCD
= (2/9)*AB*AD
=2/9*6*9
=12
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点E,F在哪里?
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