use trigonometry to find the area of each regular polygon below round your answers to the nearest tenth

To solve this, we are going to use the formula for the area of a regular polygon knowing its apothem: [tex]A=(a^2)(n)tan( \frac{180}{n} )[/tex]
where
[tex]A[/tex] is the area of the regular polygon.
[tex]a[/tex] is the apothem (the perpendicular distance from the center to a side)
[tex]n[/tex] is the number of sides of the regular polygon.
[tex]tan[/tex] is the trigonometric function tangent

We can infer from our picture that our regular polygon has 6 sides, so [tex]n=6[/tex]. We also know that the apothem (the perpendicular distance from the center to a side) of our regular polygon is 18m, so [tex]a=18m[/tex]. Lets replace those values in our formula to find [tex]A[/tex]:
[tex]A=(a^2)(n)tan( \frac{180}{n} )[/tex]
[tex]A=(18m)^2(6)tan( \frac{180}{6} )[/tex]
[tex]A=324m^2(6)tan(30)[/tex]
[tex]A=1944m^2tan(30)[/tex]
[tex]A=1122.4m^2[/tex]

We can conclude that the area of our regular polygon is 1122.4 square meters.