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".
[tex]\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}[/tex]
