Areas of Regular Polygons 11'5

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Areas of Regular Polygons11.5
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Area of An Equilateral Triangle

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Radius
Radius From the CP to a vertex on the figure n
radi per figure
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Theorem

• Theorem Any radius of a regular polygon bisects
  the angle at the vertex to which it is drawn.

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Apothem
Apothem From the CP 90 to side n apothems
per figure
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Definition

• A central angle of a regular polygon is an angle
  formed by two consecutive radii of the regular
  polygon.

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Area of a Regular Polygon

• Theorem The area A of a regular polygon whose
  apothem has length a and whose perimeter is P is
  given by

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Regular Polygon Equations
Parallelogram Trapezoid Hexagon Reg. Poly
Area Reg. Poly Perimeter

• Triangle
• Square
• Rectangle
• Rhombus or
• Kite

Regular Polygon Areas
Regular Polygon Perimeters
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Pentagon
External angle 360/n
Sum of External angles 360
Sum of Interior angles 180(n-2)
Interior angle 180(n-2)/n
Interior angle 180-Exterior angle
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Polygons

• 1.  What is the measure of an interior angle of a
  regular 9-gon?

140
11.1
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Polygons

• 2.  The measure of an interior angle of a regular
  polygon is 160. How many sides does the polygon
  have? 
• A.20
• B.18 
• C.12
• D.16

11.1
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Polygons

• 5.  The exterior angle of a regular polygon is
  32.7. Find the number of sides. 
• A.11
• B.7 
• C.10
• D.6

• 11.1

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Polygons and Circles

• 4.  A square is inscribed in a circle of radius 4
  cm. Find the area of the region that is outside
  of the pentagon and inside the circle. Round the
  answer to the nearest whole number. 

11.5
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A. 50.11 B. 26.32 C. 18.26 D. 38.37
Apr2
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Homework

• HW 11_5 Polygons.gsp