1. 11.2a Area of Regular Polygons CCSSLESSON GOALS  Identify the radius, central angle, and apothem of a polygon.  Find the measure of a polygon’s central angle  Find the area of a regular polygon ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers G GPE 7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. G C 3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

2. definition Center of a Polygon The center of its circumscribed circle. Radius of a Polygon The radius of its circumscribed circle.

3. definition Apothem of a Polygon The distance from the center to any side of the polygon. radius apothemapothem

4. definition Central Angle of a Regular Polygon An angle whose vertex is the center and whose sides contain two consecutive vertices of the polygons.

5. definition The Measure of a Central Angle of a Regular Polygon 72 o

6. Example

8. Area of a Regular Polygon 1.Draw the radii of the polygon 2.Find the measure of the central angle. 3.Draw the apothem. What happens to the central angle? 4.Find the area of the triangle. 5.Multiply by the number of triangles.

9. Area of a Regular Polygon Find the area of a regular hexagon with side length of 4 yds. 1.Divide the polygon into congruent triangles by drawing the radii of the polygon. 4 yds

10. Area of a Regular Polygon 2.Find the measure of the central angle. 4 yds Find the area of a regular hexagon with side length of 4 yds.

11. Area of a Regular Polygon 3.Draw the apothem. What happens to the central angle? 4 yds Find the area of a regular hexagon with side length of 4 yds.

12. Area of a Regular Polygon What happens to the base? 4 yds 3.Draw the apothem. Find the area of a regular hexagon with side length of 4 yds.

13. Area of a Regular Polygon 4.Find the length of the apothem. 4 yds Find the area of a regular hexagon with side length of 4 yds.

14. 4 yds Area of a Regular Polygon 5.Find the area of one inner triangle. 4 yds Find the area of a regular hexagon with side length of 4 yds.

15. Area of a Regular Polygon 6.Multiply by the number of sides/triangles. 4 yds Find the area of a regular hexagon with side length of 4 yds.

16. Area of a Regular Polygon Find the area of a square with a radius 6 units. 1.Divide the polygon into congruent triangles by drawing the radii of the polygon.

17. Area of a Regular Polygon 2.Find the measure of the central angle. Find the area of a square with a radius 6 units.

18. Area of a Regular Polygon 3.Draw the apothem. What happens to the central angle? Find the area of a square with a radius 6 units

19. Area of a Regular Polygon 4.Find the length of the apothem. Find the area of a square with a radius 6 units

20. Area of a Regular Polygon 5.Find the area of one inner triangle. Find the area of a square with a radius 6 units

21. Area of a Regular Polygon 6.Multiply by the number of sides/triangles. Find the area of a square with a radius 6 units.

22. Area of a Regular Polygon The area of a regular polygon can be found using n = the number of sides s = the length of a side a = the length of the apothem P = perimeter of the polygon

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