Warm-Up

• What is the perimeter of a regular decagon with side length s = 6?

Geometry 9-2

Developing Formulas for Circles and Regular Polygons

DefinitionsA circle is the collection of points in a plane that are a fixed distance from a point called the center of the circle. A circle is named by the symbol and its center. A has radius r = AB and diameter d = CD.

Circumference and Area

Example

Find the area and circumference of K.

Example

• What is the area of the shaded region?

mCBA = 60.00

C

B

A

4 in.

DefinitionThe center of a regular polygon is equidistant

from the vertices. The apothem is the distance

from the center to a side.

The apothem of the figure is BC.

Formula

Examples

• What is the area of a regular triangle with side length s = 4m and apothem a = 1.5m.

• What is the area of a regular octagon with side length s = 5 and apothem a = 2.