What you’ll learn:
1. To find areas of regular polygons.
2. To find areas of circles.

A= πr²
This is not the same as C=2 πr because squaring and multiplying by 2 are not the same operation!

Parts of a regular polygon radius – drawn from the center of the polygon to a vertex. The radius bisects the angle it is drawn to. (number of radii=number of sides) perimeter – sum of the measures of the sides apothem – segment drawn from the center to a side. It bisects the sides and is perpendicular to that side. (number of apothems=number of sides)
If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then A=½Pa.

In a regular polygon, the apothem and radius form a right triangle. This means that all information about right triangle applies. (Pythagorean thm., special right triangles, trig ratios)
In a regular HEXAGON, (any only a regular hexagon) the length of the radius is the same as the length of a side. Why is this? Because each angle is 120, when the radius is drawn, it creates a 30-60-90 triangle with the apothem.
In the figure, the shorter leg
60
 would be 10, so the entire side would be 20 (same as r)

Find the area of each polygon.
Round to the nearest tenth.
Find the area of a regular pentagon with a perimeter of 90 meters.
Find the area of a regular hexagon with an apothem length of 30 in.

1.
Find the area of each shaded region.
2.
15 in