10-3 Areas of Regular Polygons

Definitions Center of a regular polygon  the center of the circumscribed circle. Radius of a regular polygon  the distance from the center to a vertex. All radii of a figure are congruent. Central angle of a regular polygon  an angle formed by two radii drawn to consecutive vertices. All central angles are congruent. Apothem of a regular polygon  the perpendicular distance from the center of the polygon to a side. Every apothem of a figure is congruent

Theorem The area of a regular polygon is equal to half the product of the apothem and the perimeter. A= ½ aP Apothems are going to be found using special right triangles, and sine, cosine, tangent functions.

Find the area of a regular pentagon with perimeter of 40 centimeters.

Find the area of a regular octagon with a perimeter of 72 inches.

Find the area of a regular hexagon with apothem of 9.

Find the area of a regular polygon with 11 sides inscribed in a circle with a radius of 12.