(2014?临淄区模拟)如图,正方形ABCD的边长为2,点E在AB边上.四边形EFGB也为正方形,设△AFC的面积S为______.
∵正方形ABCD和正方形EFGB,塌州神
∴团亏AB=BC=CD=AD,EF=FG=GB=BE,
∵正方形ABCD的边长为2,
∴S
△AFC=S
梯形ABGF+S
△ABC-S
△CGF=
×(FG+AB)×BG+
×AB×BC-
×FG×CG
=
×(FG+AB)×BG+
×AB×BC-
×FG×(BC+BG)
=
×FG
2+FG+2-FG-
×FG
2=2.
故答迹信案为:2.