Find the area of a regular hexagon given the side length is 8 in. Leave your answer in exact form (with square root) and no decimals. (Use sq rt as the square root symbol.
The area of a hexagon depending on its side is given by: [tex]A= \frac{3L^2}{2tan(30)} [/tex] Rewriting we have: [tex]A= \frac{3L^2}{2 \frac{1}{\sqrt{3}}}[/tex] [tex]A = \frac{3\sqrt{3}L^2}{2} [/tex] Substituting values we have: [tex]A = \frac{3\sqrt{3}(8)^2}{2} [/tex] Rewriting the expression we have: [tex]A = \frac{3\sqrt{3}(64)}{2}[/tex] [tex]A = \frac{192\sqrt{3}}{2}[/tex] [tex]A = 96\sqrt{3}[/tex] Answer: the area of a regular hexagon given the side length is 8 in is: [tex]A = 96\sqrt{3}[/tex]
