∵ In the isosceles trapezoid ABCD, AD∨BC, ∠ B = 60, AD= 1,

∴∠C=60，∠BAD= 120，∠ADC= 120，

∫ Quadrilateral AEFG is a square,

∴∠BAG=90，

∴∠DAG=30，

∴∠DGA=30，

∵DN⊥AG,∴AN=NG，

∴ad=dg= 1,dn= 12ad= 12，

∴AN=32，

∴AG=AE=EF=FG=3，

∴BF=EFsin60 =332=2，

∠∠FGA = 90 degrees, ∠AGD=30 degrees,

∴∠FGC=60，

∫∠c = 60，

△ FGC is an equilateral triangle,

∴FC=FG=3，

∴BC=BF+FC=2+3.

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