Given: Regular pyramid KO ⊥ (ABCD) KO = 10.2, m∠AKO=38º Find: Volume

Question

Given: Regular pyramid KO ⊥ (ABCD) KO = 10.2, m∠AKO=38º Find: Volume

Answer 1

Tan AKO = AO / KO so

AO = KO Tan 38 = 10.2 Tan 38 = 7.969

Area of the right triangle ABD = OA x BD/2 = 7.969 x (2 x 7.969)/2 = 63.5

Area of the square ABCD = 2 x 63.5 = 127

Volume KABCD = Area of the base x height / 3 = 127 x 10.2 / 3 = 431.8