1. 9-2 Vocabulary Circle Center of a circle Center of a regular polygon
Apothem
Central angle of a regular polygon

2. 9-2 Developing Formulas for Circles Regular Polygons
Geometry

3. Circumference of a Circle
A circle with a diameter of d and a radius r has circumference of
d=2r

4. Area of a circle
A circle with diameter d & a radius r has area of

5. Ex. 1a.) Find the area of Circle K in terms of π

6. 1b.) Find the radius of circle J if the circumference is (65x + 14)π m

7. 1c.) Find the circumference of Circle M if the area is 25x² π ft²

8. Area of an equilateral triangle
Ex. 2) Find the area of an equilateral triangle with 10 cm sides.
Ex. Ex. 2

9. Area of a regular polygon

10. Central Angle of a Regular Polygon
Is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon. Since, a circle’s total is
then you can divide 360 by the number of sides to find the measure of each central angle of the polygon.

11. Steps for solving for Area (Hint: sketch picture )
1.) Find the “a” (apothem) either by using
a.) Trig ratios - Find central angle
Then, divide central angle by 2.
Use either sin, cos or tan to find “a”.
b.) Pythagorean Thm - If given 2 sides then, use
(Don’t forget to take if “s” is given.)
2.) Figure Perimeter , P=ns.
3.) Substitute everything into

12. Ex. 3a.) Find the area of a regular heptagon with side length of 2 ft

13. Ex. 3b) Find the Area of a regular dodecagon with side length 5 cm

14. Assignment

15. Ex. 2
A regular octagon is inscribed in a circle with radius 4 units. Find the area of the octagon.

16. Ex. 3
The bottom of a glass is a regular 12-gon with a side length of about 1.2 cm and a radius of 2.3 cm. What is the area of the bottom of the glass.

17. Area of an equilateral triangle