1. 10-5 Areas of Regular Polygons

2. 10-5 Areas of Regular Polygons
•Area of a Regular Polygon
Vocab:
Center – in the center
Radius - to a vertex
Central angle –from 2 radii
Apothem –perpendicular
from center to side

3. Areas of Regular Polygons
•Area of a Regular Polygon

4. Areas of Regular Polygons
•Area of a Regular Polygon
•Area = (area of the ∆) x (# of ∆’s)

5. Areas of Regular Polygons
•Area of a Regular Pentagon
•Area = (area of the ∆) x (# of ∆’s)
•Area = ( ½ apothem x side length) x (number of sides)

6. Areas of Regular Polygons
•Area of a Regular Pentagon
•Area = (area of the ∆) x (# of ∆’s)
•Area = ( ½ apothem x side length) x (number of sides)

7. Areas of Regular Polygons
•Area of a Regular Pentagon
•Area = (½ apothem x side length) x (number of sides)
•Area = ½ apothem x Perimeter

8. Areas of Regular Polygons
•Theorem 10-5
•The area of a regular n-gon with side length s is
half the product of the apothem a and the perimeter
P
•A = ½ aP
•OR
•A = ½ a x ns

9. Areas of Regular Polygons
•Area of a Regular Polygon
•How to figure out the apothem

10. Areas of Regular Polygons
•Area of a Regular Polygon
•How to figure out the apothem
C
B
A

11. Areas of Regular Polygons
•Area of a Regular Polygon
•How to figure out the apothem
•P-Thag Theorem
C
B
Apothem

12. Areas of Regular Polygons
•Area of a Regular Polygon
•How to figure out the apothem
tan x = __B__
apothem
C
B
x°
Apothem

13. Areas of Regular Polygons
•Area of a Regular Polygon
•How to figure out the apothem
tan x = __B__
apothem
Apothem =_ B__
tan x
C
B
x°
Apothem

14. Areas of Regular Polygons
•Area of a Regular Polygon
•How to figure out the apothem
cos x = apothem
C
Apothem = cos x
C
C
B
x°
Apothem

15. SPICSA
P 443 1-12all,
14,16