Question

Find the height and the volume of a regular hexagonal pyramid with the lateral edges 10 ft and the base edges 6 ft

Answer 1

Solution

Find the height and the volume of a regular hexagonal pyramid with the lateral edges 10 ft and the base edges 6 ft

The volume (V) of a hexagonal pyramid of base edge (a) and height (h) is:

V = (√3/2) a^2 h.

Since the base edges is a hexagon

base edge = 6ft

lateral edge = 10ft

heght -= x

Height of each triangle in the pyramid is...

h^2 + 3^2 = 10^2

$\begin{gathered} h^2=100-9 \\ h^2=91 \\ h=\sqrt{91} \\ h=9.54ft \end{gathered}$

(1) Height = 9.54ft

$\begin{gathered} V=\frac{\sqrt{3}}{2}a^2h \\ V=\frac{\sqrt{3}}{2}.6^2(9.54) \\ V=297.43ft^3 \end{gathered}$

(2) Volume = 297.43ft³