设A1C1∩B1D1=O1,根据线面垂直的判定定理可知B1D1⊥平面AA1O1,再根据面面垂直的判定定理可知故平面AA1O1⊥面AB1D1,交线为AO1,在面AA1O1内过A1作A1H⊥AO1于H,则A1H的长即是点A1到截面AB1D1的距离,在Rt△A1O1A中,利用等面积法求出A1H即可.
【解析】
如图,设A1C1∩B1D1=O1,∵B1D1⊥A1O1,B1D1⊥AA1,∴B1D1⊥平面AA1O1,
故平面AA1O1⊥面AB1D1,交线为AO1,在面AA1O1内过B1作B1H⊥AO1于H,
则易知A1H的长即是点A1到截面AB1D1的距离,在Rt△A1O1A中,A1O1=,
AO1=3,由A1O1•A1A=h•AO1,可得A1H=,
故选:C.