The first step to find the area of the hexagon is to find the apothem of it by using the following formula:
[tex]a=\frac{l}{2tan\theta}[/tex]
Where l is the sidelength and θ is half the central angle:
[tex]a=\frac{\frac{16\sqrt{3}}{3}}{2tan30}=8[/tex]
Now, find the perimeter of the hexagon by multiplying the side length by 6:
[tex]\begin{gathered} P=6\cdot\frac{16\sqrt{3}}{3} \\ P=32\sqrt{3} \end{gathered}[/tex]
Finally, find the area of the hexagon by using the following formula:
[tex]\begin{gathered} A=\frac{P\cdot a}{2} \\ A=\frac{32\sqrt{3}\cdot8}{2} \\ A=128\sqrt{3} \end{gathered}[/tex]
The area of the given hexagon is 128√3
