1. Areas of Regular Polygons
10-3

2. Warmup
Identify the number of sides for each type of polygon: 1.) undecagon 2.) decagon 3.) heptagon 4.) dodecagon 5.) pentagon

3. Definitions
radius
apothem
center
Center – the center of the circle circumscribed about the polygon
radius – a segment drawn from the center of a polygon to a vertex
apothem – a segment drawn from the center of a polygon that is perpendicular to a side
central angle – an angle formed by two radii drawn to consecutive vertices
*Every regular polygon can be broken into isosceles triangles (one equilateral)
Central angle

4. Theorem 11.6 Area of a Regular Polygon
The area of a regular n-gon with side lengths (s) is half the product of the apothem (a) and the perimeter (P), so
A = ½ aP, or A = ½ a • ns.
NOTE: In a regular polygon, the length of each side is the same. If this length is (s), and there are (n) sides, then the perimeter P of the polygon is n • s, or P = ns
The number of congruent triangles formed will be the same as the number of sides of the polygon.

5. More . . .
A central angle of a regular polygon is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon. You can divide 360° by the number of sides to find the measure of each central angle of the polygon.
360/n = central angle

6. Ex: Finding the area of a regular polygon
A regular pentagon with radius 1 unit. Find the area of the pentagon. C 1 B D 1 A

7. Draw a regular hexagon with an apothem of 4 ft
Draw a regular hexagon with an apothem of 4 ft. Find the area in simplest radical form.

8. You try…..
Find the area of a regular polygon with 9 sides and a radius of 10