Answer to Question #105043 in Geometry for Jethro

Question

A lateral edge of the hexagonal pyramid is 20m long and its base perimeter is 6m determine the volume of the pyramid and its lateral area

Answer 1

V = 1/3 * S * H

S = 1/2 * a ²  * 3 *$\sqrt {3}$

a = P / 6 = 6/6 = 1 m

S = 1.5 * $\sqrt {3}$ m²

H = $\sqrt{400-1}$ = $\sqrt{399}$ m

V = 1/3 * 1.5 * $\sqrt {3}$ * $\sqrt{399}$ = 1.5 $\sqrt{133}$ m³

h = $\sqrt{400-0.25}$ = 0.5 * $\sqrt{1599}$ m

S _l  = 0.5 * P * h = 1.5 * $\sqrt{1599}$ m²

The answer to the problem: V = 1.5 $\sqrt{133}$ m³ , S_l  = 1.5 * $\sqrt{1599}$ m²