Answer:
Step-by-step explanation:
We can find half of a side of the pentagon with the expression
[tex]tan(36\°)=\frac{s_{half} }{11}[/tex]
Because, as a regular polygon, all its sectors have the same central angle, and the apothem divides equally each sector in two equal parts.
[tex]s_{half} \approx 8[/tex]
Therefore, half of a side is 8 units long, which means each side measures 16 units.
Now, the area of a penthagon is defined by
[tex]A=\frac{p \times a}{2}[/tex]
Where [tex]p[/tex] is the perimeter and [tex]a[/tex] is the apothem. Where the perimeter is the sum of all sides, which is 80 units.
[tex]A= \frac{80 \times 11}{2} =440 \ u^{2}[/tex]
Therefore, the right answer is the second choice.
