作业帮求这个阴影面积占总面积多少...
来源：学生作业帮 编辑：拍题作业网作业帮 分类：综合作业 时间：2024/04/26 06:05:14
求这个阴影面积占总面积多少...
等边3角形.每边有个3等分点,求阴影部分面积是总面积的多少
易证 △DEF为等边三角,△BEG全等△ADK全等△CFH
△BEG∽△BAK, BE:GE=AB:AK=3:1. BE:DK=3:1
△BDH∽△BGK, BD:DH=BC:CK=3:2 (BE+ED):(DF+FH)=3:2, (3DK+ED):(ED+DK)=3:2
ED:DK=3:1
BE:ED:DK=3:3:1, 同理：CF:EF:EG=3:3:1, AD:DF:FH=3:3:1
AG:AB=3:2 S(AGC):S(ABC)=3:2, S(AGC)=2S(ABC)/3
GF:CG=4:7 S(AGF):S(AGC)=4:7 S(AGF)=4S(AGC)/7=8S(ABC)/21
EF:GF=3:4 S(AEF):S(AGF)=3:4 S(AEF)=3S(AGF)/4=2S(ABC)/7
EF:AF=1:2 S(DEF):S(AEF)=1:2 S(DEF)=S(AEF)/2=S(ABC)/7