Question

HELP PLS!!!

Find the surface area of the pyramid.

Answer 1

well, the hexagonal pyramid is really just six triangles with a base of 24 and a height of 24 as well, and a hexagonal base with an apothem of 12√3 and sides of 24.

`\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap ~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=12√(3)\\ p=\stackrel{(24)(6)}{144} \end{cases}\implies A=\cfrac{1}{2}(12√(3))(144) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{six triangles}}{6\left[ \cfrac{1}{2}(\underset{b}{24})(\underset{h}{24}) \right]}~~ + ~~\stackrel{\textit{hexagonal base}}{\cfrac{1}{2}(12√(3))(144)}}\implies 1728+864√(3) ~~ \approx ~~ \text{\LARGE 3224}~m^2`