Question

图中ABCD为矩形 其面积为S,三角形ADF,AFE,AEB的面积为S1 ,S2和S3.若S2=20,S1×S3与S的比

Answer 1

S1*S2/S=S/12,故BE×DF=S/3

CEF面积设为S4

S4=EC*FC/2

=(AB-DF)*(BC-BE)/2

=(AB*BC-AB*BE-DF*BC+DF*BE)/2

=(S-2S3-2S1+S/3)/2

=2S/3-S3-S1

S2=S-S1-S3-S4

=S-S1-S3-(2S/3-S1-S3)

=S/3

S=S2*3=20*3=60