Area of Regular Polygons Unit 11 Section 4

Area of Regular Polygons Unit 11 Section 4 Know and use the formulas for the area of regular Polygons.

Regular Polygons: Regular Polygon interior Angle Formula:

Center of a regular polygon: the center of the circumscribed circle. Radius of a regular polygon: the distance from the center to a vertex.

Central angle of a regular polygon: an angle formed by two radii drawn to consecutive vertices. Apothem of a regular polygon: (perpendicular distance from the center of the polygon to a side. Practice: Lesson 11. 4 #3

Example 1: Find the measure of a central angle for each inscribed figure. a. A square b. A regular dodecagon (12 -sided polygon) Practice 1: Find the measure of a central angle for each inscribed figure. a. A hexagon b. A octagon

Example 2: Find the perimeter and the area of a regular hexagon with apothem 6. Central Angle = 360/6 = 60° s O Triangle ∆AOX is a 30 -60 -90 could use that relationship to find ½ s then find s OR Tan(∠AOX) = (½ s)/6 Tan(30) = (½ s)/6 Practice: Lesson 11. 4 Notes #1 -2 6 A ½s X B

Theorem 11. 6: the area of a regular polygon is equal to half the product of the apothem and the perimeter. Area = ½ ap Example 3: Find the perimeter and the area of each figure a regular hexagon with apothem 6. Still need to find the length of a side and the perimeter Recall: Practice: Lesson 11. 4 Notes #4

Example 4: Find the perimeter and area of each figure. a. A regular octagon with side 5. b. A regular pentagon with radius 8. Practice: Lesson 11. 4 Notes #5 -6 Homework: Practice Worksheet 11. 4