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幼苗
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过点E作EM‖BD,交AC于M.
根据比例关系,可得:
AM∶AC = AE∶AB = 1/6 ,
AM = (1/6)AD = (1/12)AC ,
CM = CD + DM = (11/12)AC ,
MD = AD - AM = (5/12)AC ,
DH∶EM = CD∶CM = 6/11 ,
EM∶BD = AE∶AB = 1/6 ,
所以,
DH = (1/11)BD ,
△CDH面积 = (1/11)△BCD面积 = (1/22)△ABC面积 ,
△BCH面积 = (10/11)△BCD面积 = (5/11)△ABC面积 .
同理可求得:
EI = (1/10)CE ,
△AEI面积 = (1/10)△ACE面积 = (1/60)△ABC面积 ,
△ACI面积 = (9/10)△ACE面积 = (3/20)△ABC面积 .
FG = (1/4)AF ,
△BFG面积 = (1/4)△ABF面积 = (1/12)△ABC面积 ,
△ABG面积 = (3/4)△ABF面积 = (1/4)△ABC面积 .
于是可计算:
△GHI面积
= △ABC面积 - △BCH面积 - △ACI面积 - △ABG面积
= (8/55)△ABC面积 .
阴影面积
= △CDH面积 + △AEI面积 + △BFG面积
= (8/55)△ABC面积
= △GHI面积
= 1.98 (cm²)
1年前
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