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

2. Regular Polygons:
Regular Polygon interior Angle Formula:

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

4. 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

5. 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

6. 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
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

7. 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

8. 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