Areas of Regular Polygons

1
Areas of Regular Polygons

• 5.6

2
Definitions

• Center the center of a regular polygon is the
  center of the circumscribed circle
• Radius the radius of a regular polygon is the
  distance from the center to a vertex
• Apothem - the apothem of a regular polygon is the
  perpendicular distance from the center to a side

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Apothem
Center
radius
4
Theorem 5.9

• The area of a regular polygon is half the product
  of the apothem and the perimeter
• Area ½ (apothem) (perimeter)
• A ½ ap

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• First find Perimeter
• p (8)8 or 64
• a 1/2ap
• 1/2(12.3)(64)
• 393.6

12.3
8
6
Find the area of the equilateral triangle

• a ½ ap
• a?
• p?
• a3
• p18 3
• Area 1/2(3)(18 3)
• Area 46.76

60o
6
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• Ch.6 Formula Sheet
• Area of a rectangle______________________
• Area of a Square_______________________
• Area of a triangle________________________
• Area of a trapezoid_________________
• Area of a regular polygon__________________
• For triangles
• If given the radius
• Side length___r 3____
• Apothem _____ r/2__ __________
• If given the apothem
• Side length____2a 3
• For squares
• If given the radius
• Side length____ r 2______________
• area__side length (side length)________________
  
• Area of a circle_________________
• Circumference of a circle________________________
  

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• Homework
• P. 276 1-12, 15-18, 23-26