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 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

9-2: Perimeter and Area of Regular Polygons 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

Perimeter and Area of Regular Polygons Section 9–2 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

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. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

9-2: Perimeter and Area of Regular Polygons Example 4 Find the area of a regular nonagon with the perimeter of 144 in. 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons

9-2: Perimeter and Area of Regular Polygons Assignment Page 767: 12–14, 26 Page 603: 14, 15, 17, 27-31 odd Quiz Block Day 11/22/2018 10:00 PM 9-2: Perimeter and Area of Regular Polygons