Question

棱长为a的正方体ABCD-A1B1C1D1中正方体ABCD—A1B1C1D1中.求点A1到平面AMN的距离

Answer 1

求出三棱锥A-A1MN的体积和S△AMN就可以求出A1到平面AMN的距离

S△A1MN=a²/8

V=a³/24

MN=√2·a/2

取MN中点P,连A1P、AP

A1P=√2·a/4

AP=3√2·a/4

S△AMN=3a²/8

h=3V/S△AMN=a/3

即A1到平面AMN的距离为a/3