1. 6-3A Regular Polygons What are regular polygons? What is an apothem? How do you find the area of any regular polygon? How do you find the measure of one interior angle and one exterior angle of a regular polygon?

2. Regular Polygon A regular polygon is both equilateral and equiangular. Equilateral—all sides are the same length. Equiangular—all angles are the same measure.

3. Classify each polygon as equilateral, equiangular and/or regular. Equilateral Regular Equiangular

4. Regular Polygon Parts The center of a regular polygon is the point of intersection of the perpendicular bisectors of the sides. center

5. Regular Polygon Parts The segment from a vertex to the center is the radius. radius

6. Regular Polygon Parts The perpendicular segment from the center to a side is an apothem (AP uh them). apothem center

7. All of the radii of a regular polygon are congruent. Any regular polygon can be divided into congruent isosceles triangles. To find the area, you could then find the area of these triangles. OR….

8. Use the Regular Polygon Theorem The area of a regular polygon is one-half the product of its perimeter and its apothem. A = ½ap

9. Find the area of the regular pentagon. A pentagon has ___ sides. The perimeter is ___. Area = ½ (apothem)(perimeter) A = ½(6.9)(50) A = 172.5 in. 2 5 50 10 in a = 6.9 in

10. Find the area of a regular octagon An octagon has ___ sides. The perimeter is ___. Area = ½ (apothem)(perimeter) A = ½(18.1)(120) A = 1086 cm. 2 a = 18.1 cm 15cm 8 120

11. Finding one interior angle of a regular polygon THEOREM Each angle of a regular n-gon measures:

12. Find the measure of one inside angle of a regular pentagon. A pentagon has 5 sides, so n = 5

13. Finding one exterior angle of a regular polygon THEOREM Each exterior angle of a regular n-gon measures:

14. Find the measure of one exterior angle of a regular hexagon. A hexagon has ____ sides. n = 6 6

15. What are regular polygons? A regular polygon is both equilateral and equiangular. What is an apothem? The perpendicular segment from the center to a side is an apothem (AP uh them). How do you find the area of any regular polygon? A = ½ap How do you find the measure of one interior angle and one exterior angle of a regular polygon?

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