Check the picture below.let's recall that a circle has a total of 360°, and if we draw two radii from the center of the hexagon, the angle at the center made by those two radii will be 60°, because the hexagon will split the 360° in 6 even pieces, 360/6 = 60.anyhow, if we use half of that triangle made by two radii, we'll end up with a 30-60-90 triangle, as you see in the picture, and thus we can use the 30-60-90 rule.so, when doing so, notice, each side of the hexagon is 8 units long, therefore, the perimeter of the hexagon is then 8*6 = 48.[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=4\sqrt{3}\\ p=48 \end{cases}\implies A=\cfrac{1}{2}(4\sqrt{3})(48)\implies A=96\sqrt{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 166.28~\hfill[/tex]