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( (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( (180)/(n) )`

`A=(18m)^2(6)tan( (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.