. ▁A ▁point ▁called ▁a pe x ▁is ▁located ▁outside ▁the ▁hyper plane ▁and ▁gets ▁connected ▁to ▁all ▁the ▁vertices ▁of ▁the ▁poly to pe ▁and ▁the ▁distance ▁of ▁the ▁a pe x ▁from ▁the ▁hyper plane ▁is ▁called ▁height . ▁This ▁construct ▁is ▁called ▁a ▁n - dimensional ▁hyper py ram id . ▁ ▁A ▁normal ▁triangle ▁is ▁a ▁ 2 - dimensional ▁hyper py ram id , ▁the ▁normal ▁py ram id ▁is ▁a ▁ 3 - dimensional ▁hyper py ram id ▁and ▁the ▁pent ach or on ▁or ▁t etra hed ral ▁py ram id ▁is ▁a ▁ 4 - dimensional ▁hyper py ram id ▁with ▁a ▁t etra hed ron ▁as ▁base . ▁ ▁The ▁n - dimensional ▁volume ▁of ▁a ▁n - dimensional ▁hyper py ram id ▁can ▁be ▁computed ▁as ▁follows : ▁ ▁Here ▁ ▁denotes ▁the ▁n - dimensional ▁volume ▁of ▁the ▁hyper py ram id , ▁A ▁the ▁( n   −   1 )- dimensional ▁volume ▁of ▁the ▁base ▁and ▁h ▁the ▁height , ▁that ▁is ▁the ▁distance ▁between ▁the ▁a pe x ▁and ▁the ▁( n   −   1 )- dimensional ▁hyper plane ▁containing ▁the ▁base ▁A . ▁For ▁n   =   2 ,   3 ▁the ▁formula ▁above ▁yields ▁the ▁standard ▁formulas ▁for ▁the ▁area ▁of ▁a ▁triangle ▁and ▁the ▁volume ▁of ▁a ▁py ram id . ▁ ▁References ▁ ▁A . ▁M . ▁Math ai : ▁An ▁Introduction ▁to ▁Ge omet rical ▁Pro b ability . ▁C RC ▁Press