Question

A regular hexagonal prism has an edge length 12 cm, and height 10 cm. Identify the volume of the prism to the nearest tenth.

Answer 1

Check the picture below.

so the volume will simply be the area of the hexagonal face times the height.

`\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( (180)/(n) \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( (180)/(6) \right) \\\\\\ A=216\cot(30^o)\implies A=216√(3) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216√(3))}~~\stackrel{height}{(10)}\implies 2160√(3)~~\approx ~~3741.2~cm^3`