1. 9-2: Perimeter and Area of Regular Polygons
Sector Area
The area of a sector is a fraction of the circle containing the sector.
Sector Area of a Circle: 𝑨=𝝅 𝒓 𝟐 𝒎 𝟑𝟔𝟎 where m is the given angle
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9-2: Perimeter and Area of Regular Polygons

2. 9-2: Perimeter and Area of Regular Polygons
Example 5
Find the area of sector ABC. Give answers in terms of  and rounded to the nearest ten-thousandth.
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9-2: Perimeter and Area of Regular Polygons

3. 9-2: Perimeter and Area of Regular Polygons
Example 6
Identify the radius of a circle if the sector area is 1/16  ft2 and the angle sector area is 90 degrees. If needed, rounded to the nearest ten-thousandth.
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9-2: Perimeter and Area of Regular Polygons

4. 9-2: Perimeter and Area of Regular Polygons
Example 7
Determine the angle measure if the sector area is 4  in2 and the radius is 6 inches. If needed, rounded to the nearest ten-thousandth.
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9-2: Perimeter and Area of Regular Polygons

5. 9-2: Perimeter and Area of Regular Polygons
Your Turn
Identify the radius of a circle if the sector area is 1/32 ft2 and the angle sector area is 180 degrees. If needed, rounded to the nearest ten-thousandth.
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9-2: Perimeter and Area of Regular Polygons

6. 9-2: Perimeter and Area of Regular Polygons
Page 603 and 767
10)
49 yards
11)
5 meters
12)
𝟏𝟎  𝒇𝒆𝒆𝒕
40)
𝟏  𝒎
19)
𝟐𝟓 18  𝒎𝒎
20)
𝟒 3  𝒎
21)
 10 𝒇𝒕
27) 𝟏𝟐
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9-2: Perimeter and Area of Regular Polygons

7. 9-2: Perimeter and Area of Regular Polygons
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9-2: Perimeter and Area of Regular Polygons

8. Perimeter and Area of Regular Polygons
Section 9–2
Geometry PreAP, Revised ©2014
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9-2: Perimeter and Area of Regular Polygons

9. Definitions and Formulas
The center of a regular polygon is equidistant from the vertices.
Apothem is the distance from the center to a side.
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 360/n
The area of a regular polygon with an apothem is 𝐴= 𝟏 𝟐 𝒂𝑷 where a is the apothem and P is the perimeter
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9-2: Perimeter and Area of Regular Polygons

10. 9-2: Perimeter and Area of Regular Polygons
Steps
Divide 360 and the sides of the polygon.
Take the tangent ratio of the triangle to determine the apothem (adjacent leg). Make sure to divide the answer in part A by 2, since it is half that angle.
Apply it to the equation, A = 1/2aP where a is the apothem and P is perimeter. Perimeter = (Sides) * 2
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9-2: Perimeter and Area of Regular Polygons

11. 9-2: Perimeter and Area of Regular Polygons
Example 1
Find the area of regular heptagon with side length 2 ft. Round to 4 decimal places.
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9-2: Perimeter and Area of Regular Polygons

12. 9-2: Perimeter and Area of Regular Polygons
Example 2
Find the area of a regular octagon with a side length of 4 cm. Round to 4 decimal places.
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9-2: Perimeter and Area of Regular Polygons

13. 9-2: Perimeter and Area of Regular Polygons
Your Turn
Find the area of a regular dodecagon with side length 5 cm. Round to 4 decimal places.
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9-2: Perimeter and Area of Regular Polygons

14. 9-2: Perimeter and Area of Regular Polygons
Example 3
Find the area of an equilateral triangle with an apothem of 2 feet. Round to 4 decimal places.
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9-2: Perimeter and Area of Regular Polygons

15. 9-2: Perimeter and Area of Regular Polygons
Example 4
Find the area of a regular nonagon with the perimeter of 144 in.
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9-2: Perimeter and Area of Regular Polygons

16. 9-2: Perimeter and Area of Regular Polygons
Assignment
Page 767: 12–14, 26 Page 603: 14, 15, 17, odd Quiz Block Day
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9-2: Perimeter and Area of Regular Polygons