极难的数学题The hexagon ABCDEF is convex and opposite sides are pa

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极难的数学题
The hexagon ABCDEF is convex and opposite sides are parallel.Show that the triangles ACE and BDF have equal area.
（用中文回答）

在凸六边形ABCDEF内作平行四边形ABCP,CDEQ,EFAR,因为六边形三组对边平行,所以,A,P,R在一直线上,C,Q,P在一直线上,E,R,Q在一直线上.
S(ABCDEF)=S(ABCP)+S(CDEQ)+S(EFAR)+S(PQR),
S(ACE)=S(ABCP)/2+S(CDEQ)/2+S(EFAR)/2+S(PQR).
又在六边形ABCDEF内作平行四边形FABM,BCDN,DEFL,因为六边形三组对边平行,所以,F,L,M在一直线上,B,M,N在一直线上,D,N,L在一直线上.
S(ABCDEF)=S(FABM)+S(BCDN)+S(DEFL)+S(LMN),
S(BDF)=S(FABM)/2+S(BCDN)/2+S(DEFL)/2+S(LMN).
易知PQ=LM=|AB-DE|,QR=MN=|AF-CD|,RP=NL=|BC-EF|,
所以,S(PQR)=S(LMN).
S(ABCP)+S(CDEQ)+S(EFAR)=S(FABM)+S(BCDN)+S(DEFL),
S(ACE)=S(BDF).

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