Given:
Given that the side of the regular polygon is 16 feet.
We need to determine the area of the polygon.
Area of the polygon:
The area of the polygon can be determined using the formula,
[tex]Area =\frac{s^2 n}{4 \ tan \frac{180}{n}}[/tex]
where n is the number of sides,
s is the side length.
Substituting n = 3 and s = 16, we get;
[tex]Area =\frac{16^2 (3)}{4 \ tan \frac{180}{3}}[/tex]
Simplifying, we get;
[tex]Area =\frac{(256) (3)}{4 \ tan \ 60}[/tex]
[tex]Area = \frac{768}{6.928}[/tex]
Dividing, we get;
[tex]Area = 110.85[/tex]
Rounding off to the nearest tenth, we have;
[tex]Area = 110.9[/tex]
Thus, the area of the regular polygon is 110.9 square units.
