Kneel for the quadrilateral problem of second grade mathematics.

The area of quadrilateral EGHF is one third of quadrilateral ABCD;

Prove:

Connect BE, EH, DH and BD as shown in the figure.

BG = GH

∴S△BGE=S△HGE

Similarly EF=DF, S△DHF=S△EHF.

∴S△BGE+S△DHF=S△HGE+S△EHF=S quadrilateral EGHF

∴S quadrilateral EGHF= 1/2? S quadrilateral bed

∵? DE=2AE

∴DE=2/3DA

∴S△BDE=2/3？ S△ABD

Similarly BH=2/3BC, S△BDH=2/3? S△BCD

∴S△BDE+S△BDH=2/3S△ABD+2/3？ S△BCD

∴S quadrilateral BEDH=2/3S quadrilateral ABCD

∴S quadrilateral EGHF= 1/3? S quadrilateral ABCD

For another reference answer:/blog/static/25253498200955331775/

Ask if you don't understand!