Section 11-4Areas of Regular

Polygons

Given any regular polygon, you can circumscribe a circle about it.

Center of a regular polygon

• is the center of the circumscribed circleExample:

Radius of a regular polygon

• is the distance from the center to a vertex

Example:

Central angle of a regular polygon

• is an angle formed by two radii drawn to consecutive vertices.

Example:

To find the Measure of a Central Angle of a Regular Polygon:

**n = the number of sides

n360

= Central Angle

1

63601m

601m

Find the measure of a central angle for each inscribed figure.

1. A square2. A regular octagon3. A regular pentagon4. A regular Decagon

9045

3672

apothem of a regular polygon

• Is the (perpendicular) distance from the center of the polygon to a side.

Example:

Theorem 11-6• The area of a regular polygon

is equal to half the product of the perimeter and the apothem.

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