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 square A regular dodecagon (12-sided polygon) Practice 1: Find the measure of a central angle for each inscribed figure. A hexagon 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 6 A B X ½ s Practice: Lesson 11.4 Notes #1-2

Still need to find the length of a side and the perimeter 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 regular octagon with side 5. A regular pentagon with radius 8. Practice: Lesson 11.4 Notes #5-6 Homework: Practice Worksheet 11.4