Areas of Regular Polygons

Geometry

Unit 4, Lesson 3

Regular Polygons

• Regular Polygon is any Polygon that is both equiangular and equilateral.

• You can circumscribe a circle about any regular polygon.

Regular Polygons (cont.)

• The center of a regular polygon is the center of the circumscribed circle.

Center

Regular Polygons (cont.)

• The radius of a regular polygon is the distance from the center to a vertex

CenterRadius

Regular Polygons (cont.)

• The apothem of a regular polygon is the perpendicular distance from the center to a side

CenterRadius

Apothem

Theorem 5-9:Area of a Regular Polygon

• The area of a regular polygon is half the product of the apothem and the perimeter.

• A = ½ap

a

p

Example:

• Find the area of a regular decagon with a 12.3 in apothem and 8 in sides?– First: What is the number of sides?– Second: Find the perimeter.– Third: Plug into the formula

• Answer: 492 in2

Example:

• Find the area of a regular pentagon with the sides of 11.6 cm and apothem of 8 cm

• Area = ½ (8cm) (11.6 x 5) =232 cm2