Chapter 11.6 Notes: Areas of Regular Polygons Goal: You will find areas of regular polygons inscribed in circles.

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Presentation transcript:

Chapter 11.6 Notes: Areas of Regular Polygons Goal: You will find areas of regular polygons inscribed in circles.

The center of the polygon and the radius of the polygon are the center and the radius of its circumscribed circle. The distance from the center to any side of the polygon is called the apothem of the polygon. A central angle of a regular polygon is an angle formed by two radii drawn to consecutive vertices of the polygon.

Ex.1: In the diagram, ABCDE is a regular pentagon inscribed in circle F. Find each angle measure. a. b. c.

Theorem Area of a Regular Polygon: The area of a regular n-gon with side lengths, s, is one half the product of the apothem, a, and the perimeter, P. a = apothem; P = Perimeter

Ex.2: You are decorating the top of a table by covering it with small ceramic tiles. The table top is a regular octagon with 15 inch sides and a radius of about 19.6 inches. What is the area you are covering?

Ex.3: A regular nonagon is inscribed in a circle with radius 4 units. Find the perimeter and area of the nonagon.

Find the perimeter and area of the regular polygon. Ex.4: Ex.5:

Find the perimeter and area of the regular polygon. Ex.6:

Ex.7: A regular decagon is inscribed in a circle with radius 8 units. Find the perimeter and area of the decagon.