The length of one side edge of a triangular pyramid is 16 cm, the length of the opposite edge is 18 cm, and the length of the other four edges is 17 cm

The length of one side edge of a triangular pyramid is 16 cm, the length of the opposite edge is 18 cm, and the length of the other four edges is 17 cm

As shown in the figure, take the midpoint e of AD, connect CE, be ∵ AC = CD = 17, de = 8, CE2 = 172-82 = 225, be = CE, ∵ take the midpoint F of BC, connect EF, EF is the height on the edge of BC, EF = CE2 − CF2 = 152 − 92 = 12. ∵ s △ BCE = 108. ∵ AC = CD = 17cm, e is the midpoint of AD, CE ⊥ ad, similarly be ⊥ ad, ≁ Da ⊥ plane bce.. The triangular pyramid can be divided into two triangular pyramids with the bottom BCE and the height of AE and de. ≁ VA- BCD=VA-BCE+VD-BCE=2•13S△BCE•AE=2×13×108×8=576（cm3）．