1. Chapter 7 Lesson 5 Objective: Objective: To find the area of a regular polygon

2. You can circumscribe a circle about any regular polygon. You can circumscribe a circle about any regular polygon. RegularPolygons Center of a Regular Polygon is the center of the circumscribed circle. Center of a Regular Polygon is the center of the circumscribed circle. Radius is the distance from the center to a vertex. Radius is the distance from the center to a vertex. Apothem is the perpendicular distance from the center to a side Apothem is the perpendicular distance from the center to a side

3. Example 1: Finding Angle Measures 1 2 3 Find the measure of each numbered angle. 3

4. Example 2: Finding Angle Measures 1 3 2 3 Find the measure of each numbered angle.

5. Example 3: Finding Angle Measures Find the measure of each numbered angle. 1 2 3

6. Example 4: Finding Angle Measures 1 2 3 Find the measure of each numbered angle. 2

7. Theorem 7-12: Theorem 7-12: Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter. a Perimeter is the measurement around the polygon

8. Example 5: Finding the Area of a Regular Polygon Step 1: Step 1: Find the perimeter. # of Sides: 6 p=ns p=6(6) p=36 Step 2: Step 2: Find the area.

9. Example 6: Finding the Area of a Regular Polygon Step 1: Step 1: Find the perimeter. # of Sides: 6 p=ns p=6(16) p=96 Step 2: Step 2: Find the area.

10. Example 7: Finding the Area of a Regular Polygon Step 1: Step 1: Find the perimeter. # of Sides: 4 p=ns p=4(4) p=16 Step 2: Step 2: Find the area.

11. Example 8: Finding the Area of a Regular Polygon Look at your notes from yesterday what kind of triangle do you have? 30° - 60° - 90° 60° 30° Remember that 30 is only half the base the whole base is 60 Find the perimeter. # of Sides: 3 p=ns p=3(60) p=180

12. Example 9: Finding the Area of a Regular Polygon Look at your notes from yesterday what kind of triangle do you have? 45° - 45° - 90° Remember that 5 is only half the base the whole base is 10 Find the perimeter. # of Sides: 4 p=ns p=4(10) p=40 45°

13. Example 10: Finding the Area of a Regular Polygon Look at your notes from yesterday what kind of triangle do you have? 30° - 60° - 90° 60° 30° Remember LL is your apothem. Find the perimeter. # of Sides: 3 p=ns p=3(12) p=36 12 66

14. Assignment: Page 382 #1-18; 35-40