To the nearest tenth, find the volume of a regular hexagonal pyramid with base edges 12 cm long and height 15 cm.

Answer 1

V = ⅓Bh

Base Area (B)

B = ½P×a

where P = 6×12 = 72 cm

a = (√3/2)(12) = 6√3 cm

So base area (B) is given by

B = ½(72)×(6√3) = 216√3 cm²

V = ⅓216√3×15 = 1080√3 ≈ 1870.6 cm³

Answer 2

V = 1/3Bh

B = 6·(12²√3·3/2) = 1296√3 cm²; V = 1/3·1296√3·15 = 6480√3 cm³