(i) When the G point is the midpoint of AF, such as the Σ plane ABCD. ..

Take the midpoint H of AD, connect GH, GE and BH, and then

∫GH∨DF，GH= 12DF，

∴GH∥BE and GH=BE,

∴ Quadrilateral BEGH is a parallelogram,

∴EG∥BH，

∵BH？ Plane ABCD, EG? Plane ABCD,

∴EG∥ plane abcd；;

(2) Connect BD from V=VA-BDFE+V C-BDFE=2VA-BDFE=2? 13? 12(a+2a)？ Answer? 32a=32a3。