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Anarel [89]
3 years ago
5

The base of a regular pyramid is a hexagon.

Mathematics
1 answer:
Anastaziya [24]3 years ago
5 0
Check the picture below.

since the triangle is a 30-60-90 triangle, we can use the 30-60-90 rule.

now, we know half-side is "b", which is 7, meaning the length of a side in that hexagon is 7+7 or 14.

Since there are 6 sides the "perimeter", namely the sum of its sides is 14*6, or 84.  The length from the center of the regular polygon to a side is the "apothem".

\bf \textit{area of a regular polygon}\\\\
A=\cfrac{1}{2}ap~~
\begin{cases}
a=apothem\\
p=perimeter\\
-------\\
a=7\sqrt{3}\\
p=84
\end{cases}\implies A=\cfrac{1}{2}(7\sqrt{3})(84)
\\\\\\
A=294\sqrt{3}

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