Areas of Regular Polygons 10-3

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

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

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.

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

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

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.

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