ANSWER
[tex] 96 \sqrt{3} {cm}^{2} [/tex]
EXPLANATION
The area of a regular polygon is
[tex]Area= \frac{1}{2} ap[/tex]
where 'a' is the apothem of the polygon and 'p' is the perimeter of the polygon.
From the diagram,
[tex] \sin(60) = \frac{a}{8} [/tex]
a=8sin(60)
[tex]a = 4 \sqrt{3} [/tex]
[tex] \cos(60) = \frac{l}{8} [/tex]
[tex]l = 8 \cos(60) [/tex]
[tex]l = 4[/tex]
The length of one side of the hexagon is 2×4=8.
The perimeter of the hexagon is
p=6×8=48
The area of the hexagon is
[tex] = \frac{1}{2} \times 4 \sqrt{3} \times 48[/tex]
[tex] = 96 \sqrt{3} {cm}^{2} [/tex]
