In a regular triangular pyramid p-abc, if the three side edges are perpendicular to each other and the side edge length is a, then the distance from point P to plane ABC is () A. aB. 22aC. 33aD. 3a

In a regular triangular pyramid p-abc, if the three side edges are perpendicular to each other and the side edge length is a, then the distance from point P to plane ABC is () A. aB. 22aC. 33aD. 3a

Suppose the distance between point P and plane ABC is h, then ∵ three side edges are vertical in two, and the side edge length is a, ∵ AB = BC = AC = 2A, ∵ s △ ABC = 32a2. According to va-pbc = vp-abc, we can get 13 × 12 × A3 = 13 × 32a2 × h, ∵ H = 33A, that is, the distance between point P and plane ABC is 33A, so we choose: C