Answer to Question #105046 in Geometry for Jethro

Question

A lateral edge of the hexagonal pyramid is 2.0m long and its base perimeter is 6m determine the volume of the pyramid and its lateral area

Answer 1

Volume of Hexagonal pyramid is given by $\dfrac{\sqrt3}{2}a^2h$ ; where a is the base edge and h is the height

base perimeter = 6*a

6=6*a

a=1 m

lateral edge =$\sqrt{a^2+h^2}$ $=\sqrt{1^2+h^2}=2,$

$h=\sqrt{3}$

Volume = $\dfrac{\sqrt3}{2}a^2h$ =$\dfrac{\sqrt3}{2}1^2\sqrt3=3/2$

Lateral surface area = $3a\sqrt{h^2+\dfrac{3a^2}{4}}=3*1*\sqrt{3+3/4}=3\sqrt{15}/2$