Answer:
The area of the hexagon is [tex]1,014\sqrt{3}\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of a regular hexagon is equal to
[tex]A=\frac{1}{2}Pa[/tex]
where
P is the perimeter
a is the apothem
Find the length side of the hexagon
Let
b-----> the length side of the hexagon
Remember that
The formula to calculate the length side given the apothem is equal to
[tex]b=\frac{2a}{\sqrt{3}}[/tex]
we have
[tex]a=13\sqrt{3}\ ft[/tex]
substitute
[tex]b=\frac{2(13\sqrt{3})}{\sqrt{3}}[/tex]
[tex]b=26\ ft[/tex]
Find the perimeter P
[tex]P=6b=6(26)=156\ ft[/tex]
Find the area of the hexagon
[tex]A=\frac{1}{2}(156)(13\sqrt{3})=1,014\sqrt{3}\ ft^{2}[/tex]
