如图,四棱柱ABCD-A1B1C1D1的底面ABCD为正方形,侧棱与底面边长均为2a,且∠A1AD=∠A1AB=60°,则侧棱AA1和截面B1D1DB的距离是_.

问题描述:

如图,四棱柱ABCD-A1B1C1D1的底面ABCD为正方形,侧棱与底面边长均为2a,且∠A1AD=∠A1AB=60°,则侧棱AA1和截面B1D1DB的距离是______.

由题意知平面B1D1DB垂直于A1ACC1连A1D,A1B,A1C1,AC设A1C1交B1D1于O1点AC交BD于O点∵ABCD为正方形∴BD=A1C1=22a∴A1O1=2a又∠A1AD=∠A1AB=60,∴A1D=A1B=2aA1D2+A1B2=B1D12则△A1BD为等腰直角三角形则A1O=2a=A1O1...