1. 10-2 Developing Formulas Circles and Regular Polygons Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Holt Geometry

2. Warm Up Find the unknown side lengths in each special right triangle.
1. a 30°-60°-90° triangle with hypotenuse 2 ft
2. a 45°-45°-90° triangle with leg length 4 in.
3. a 30°-60°-90° triangle with longer leg length 3m

3. Objectives
Develop and apply the formulas for the area and circumference of a circle.
Develop and apply the formula for the area of a regular polygon.

4. Vocabulary circle center of a circle center of a regular polygon
apothem
central angle of a regular polygon

6. Example 1A: Finding Measurements of Circles
Find the area of K in terms of .
A = r2
Area of a circle.
Divide the diameter by 2 to find the radius, 3.
A = (3)2
A = 9 in2
Simplify.

7. Always wait until the last step to round.
The  key gives the best possible approximation for  on your calculator.
Always wait until the last step to round.
Helpful Hint

8. Example 2: Cooking Application
A pizza-making kit contains three circular baking stones with diameters 24 cm, 36 cm, and 48 cm. Find the area of each stone. Round to the nearest tenth.
24 cm diameter
36 cm diameter
48 cm diameter
A = (12)2
A = (18)2
A = (24)2
≈ cm2
≈ cm2
≈ cm2

9. Check It Out! Example 2
A drum kit contains three drums with diameters of 10 in., 12 in., and 14 in. Find the circumference of each drum.
10 in. diameter in. diameter in. diameter
C = d
C = d
C = d
C = (10)
C = (12)
C = (14)
C = 31.4 in.
C = 37.7 in.
C = 44.0 in.

10. The center of a regular polygon is equidistant from the vertices
The center of a regular polygon is equidistant from the vertices. The apothem is the distance from the center to a side. A central angle of a regular polygon has its vertex at the center, and its sides pass through consecutive vertices. Each central angle measure of a regular n-gon is
Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE.

12. Example 3A: Finding the Area of a Regular Polygon
Find the area of regular heptagon with side length 2 ft to the nearest tenth.
Step 1: Draw Δ & Label
Step 2: Central Angle
Step 3: Make Right Δ & Label
Step 4: Use Trig
Tan(25.7o) = 1/a
51.4o
25.7o
Step 5: Plug in
A=½aP 1 2

13. Example 3B: Finding the Area of a Regular Polygon
Find the area of a regular dodecagon with side length 5 cm to the nearest tenth.

14. Check It Out! Example 3
Find the area of a regular octagon with a side length of 4 cm.

15. Examples:
Find each measurement.
1. the area of D in terms of 
A = 49 ft2
2. the circumference of T in which A = 16 mm2
C = 8 mm

16. Warm Up – 11/18/13
Find each measurement.
3. Speakers come in diameters of 4 in., 9 in., and 16 in. Find the area of each speaker to the nearest tenth.
A1 ≈ 12.6 in2 ; A2 ≈ 63.6 in2 ; A3 ≈ in2
Find the area of each regular polygon to the nearest tenth.
4. a regular nonagon with side length 8 cm
A ≈ cm2
5. a regular octagon with side length 9 ft
A ≈ ft2

17. Classwork/Homework:
Area of Regular Polygons W/S