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serg [7]
3 years ago
8

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

Mathematics
1 answer:
Stels [109]3 years ago
8 0
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( \frac{180}{n} \right)\qquad 
\begin{cases}
n=\textit{number of sides}\\
s=\textit{length of a side}\\
\frac{180}{n}=\textit{angle in degrees}\\
----------\\
n=6\\
s=4
\end{cases}\\\\\\ A=\cfrac{1}{4}\cdot  6\cdot  4^2\cdot  cot\left( \frac{180}{6} \right)

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

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