Question

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

Answer 1

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

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

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