Question

a pyramid has a regular hexagonal base with side length of 4 and a slant height of 6. what is the total area of the pyramid

Answer 1

so hmm notice the picture below

the pyramid itself, is really, just one regular hexagon, at the bottom
and 6 triangles, stacked up at each other at the edges

now, if you just get the area of the regular hexagon, and the 6 triangles, add them up, that'd be the total surface area of the pyramid then

`\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}\cdot n\cdot s^2\cdot cot\left( (180)/(n) \right)\qquad \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\ (180)/(n)=\textit{angle in degrees}\\ ----------\\ n=6\\ s=4 \end{cases}\\\\\\ A=\cfrac{1}{4}\cdot 6\cdot 4^2\cdot cot\left( (180)/(6) \right)`

now, for the triangles, well, area of a triangle is 1/2 bh, as you'd know, and you have both