Section 11.6 Notes. Regular Polygon and its Parts.

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Presentation transcript:

Section 11.6 Notes

Regular Polygon and its Parts

A regular polygon is an equilateral and equiangular polygon. E C D BA

The center of a regular polygon is the center of the circumscribed circle. Pt. O is the center of regular pentagon ABCDE. A B E C D O

The radius of a regular polygon is a segment connecting its center with a vertex. A B E C D O

How many radii does a regular pentagon have? 5 radii How many radii will any regular polygon have? The number of sides

An apothem of a regular polygon is the distance from the center to the side of the regular polygon. A B E C D O F

A central angle of a regular polygon is an angle whose vertex is the center of the polygon and whose sides contains consecutive vertices of the polygon. A B E C D O

1.Draw a regular triangle, a regular quadrilateral, and a regular hexagon. 2.Draw all the central angles of each of the regular polygons. 3.What must be true of all central angles of a regular polygon and what is the sum of these angles? They are congruent. Their sum is 360 .

4.Find the measure of one central angle of each of the regular polygons from #1. regular triangle is 120° regular quadrilateral is 90° regular hexagon is 60°

5.Find measure of one central angle of a regular n-gon.

Example 1 Find the measure of a central angle of the following regular polygons: a)a regular pentagon

c)a regular 20-gon b)a regular octagon

Find the apothem and radius of each of the following regular polygons. Example 2

1.a regular triangle with a side length of a r 30  60  6

2.a regular quadrilateral with a side length of  a r 20 10

3.a regular hexagon with a side length of  a r 8 4

Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter of the regular polygon.

A B E C D O a s

Example 3 Find the area of each of the following regular polygons. 1.a regular triangle with a side length of 18 in. 18 in. a 30  9

2.a regular quadrilateral with a side length of 12 ft. using the area of a regular polygon formula 45  a 12 ft. 6

3.a regular hexagon with a side length of 6 cm 60  a 6 cm. 3

Example 4 Find the area of a regular octagon with side length of 14 cm to the nearest centimeter. 14 cm  a

Example 5 Find the area of a regular pentagon with side length of 12 cm. to the nearest hundredth. a 12 cm 