Area of Regular Polygons Teacher Notes Area = ½ (apothem)(perimeter) Vocabulary: Apothem 10/28/10 ©Evergreen Public Schools 2010

2-7 Solving Equations With Algebra Tiles powerpoint Learning Target I can find the area of regular polygons. What is a regular polygon? M2.3.K Know, prove, and apply theorems about properties of quadrilaterals and other polygons. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Launch How do you find the area of a triangle Find the measure of one interior angle of a regular hexagon. Find the area of the triangle. A = ½ bh ((n – 2)180)/n (( 4)180)/6 = 60 h = 4(tan 54) = 1.3764 A = ½ (1.3764) (8) = 22.02 cm^2 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Explore ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Equilateral Triangle Find the area of the equilateral triangle. About 27.7 cm^2 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Equilateral Triangle Explain the process you used to find the area. Use 30-6-90 to find height. A = ½ (8)(4 sqrt 2) Or tan 60 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Regular Hexagon Find the area of the regular hexagon. About 166.28 cm^2 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Regular Hexagon Explain the process you used to find the area. About 166.28 cm^2 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 It’s the Write Time What does the process of the find the areas of the triangle and hexagon have in common?   Debrief the class. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Regular Octagon Find the area of the regular hexagon. About 309.02 cm^2 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Regular Octagon Explain the process you used to find the area. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Regular Pentagon Find the area of the regular hexagon. About 110.11 cm^2 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Regular Pentagon Explain the process you used to find the area. Watch for the methods they used. ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 It’s the Write Time What do the processes of the find the areas of the hexagon, octagon and pentagon have in common? ©Evergreen Public Schools 2010

How does this formula match your process? Area of a Regular Polygon The area of a regular polygon is given by the formula below. Area = (½)(apothem)(perimeter) How do we find the apothem? apothem = ½ (n)(tan (1/2 interior angle)   Debrief the class. ©Evergreen Public Schools 2010

Team Practice Use the formula Area = (½)(apothem)(perimeter) Find the area of a regular decagon with side length of 8 cm. Find the area of a regular hexagon with side length of 8 cm. a = 12.3107 Area = 492.43 cm2 a = 6.9282 Area = 166.27 cm2 ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 2-7 Solving Equations With Algebra Tiles powerpoint Learning Target 5 3 1 2 4 Did you hit the target? I can find the area of regular polygons. Rate your understanding of the target from 1 to 5. 5 is a bullseye! ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Practice Area of Regular Polygons ©Evergreen Public Schools 2010

©Evergreen Public Schools 2010 Ticket Out Find the area of a regular 12-sided polygon with sides 8 cm. Interior angle = 150 a = ½ (8) tan(75) = 14.9282 Area = 716.55 cm2 ©Evergreen Public Schools 2010