Answer:
The area of the hexagon is [tex]96\sqrt{3}\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the hexagon is equal to
[tex]A=\frac{1}{2}Pa[/tex]
where
P is the perimeter of the hexagon
a is the apothem
Find the Perimeter P
[tex]P=6(8)=48\ cm[/tex]
Find the apothem a
[tex]a=(8)sin(60\°)[/tex]
[tex]a=8(\frac{\sqrt{3}}{2})=4\sqrt{3}\ cm[/tex]
Find the area of the hexagon
[tex]A=\frac{1}{2}(48)(4\sqrt{3})=96\sqrt{3}\ cm^{2}[/tex]
