如图所示,在正方形ABCD中,AO⊥BD,OE,FG,HI都垂直于AD,EF,GH,IJ都垂直于AO,若已知S△AIJ=1,则正方形ABCD的面积为_.

问题描述:

如图所示,在正方形ABCD中,AO⊥BD,OE,FG,HI都垂直于AD,EF,GH,IJ都垂直于AO,若已知S△AIJ=1,则正方形ABCD的面积为______.

在Rt△AIJ中,∵S△AIJ=12(IJ)2=1∴IJ=2在Rt△IJH中,IH=2IJ=2;在Rt△IHG中,GH=2IH=22;在Rt△GHF中,GF=2GH=4;在Rt△GFE中,EF=2GF=42;在Rt△EFO中,OE=ED=2EF=8;∴AD=2ED=16∴正方形ABCD的面积为:162=256...