Areas of Regular Polygons

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Areas of Regular Polygons

• Presented by Ms. Bernstein
• Edited by Mrs. Stoops

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Objectives

• Find the area of a regular polygon

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Regular Polygons

• What is a regular polygon?

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Given any regular polygon, you can circumscribe a
circle about it
Def The center of a regular polygon is the
center of the circumscribed circle.
Def The radius of a regular polygon is the
distance from center to a vertex.
Def A central angle of a regular polygon is an
angle formed by joining two radii to consecutive
vertices.
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• Def The distance from the center to any side of
  the polygon is called the apothem of the polygon.
  The apothem is the height of a triangle between
  the center and two consecutive vertices of the
  polygon.

What do we know about the apothem of the polygon?
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The apothem of a regular polygon
Theorem The area of a regular polygon A ½
(apothem) (Perimeter)
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Proof
a
s
A polygon with n sides has n triangles each A ½
(a) (s) Area (whole) n ½ as ½ (a)(ns) ½
(a) (p)
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Example Find the perimeter and area of a regular
hexagon with apothem 6.
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Example Find the perimeter and area of an
equilateral triangle with apothem 8.
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Example Find the perimeter and area of a regular
hexagon with side 12.
12
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Find the Area of the Regular Pentagon
Perimeter is 30
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Individual Practice

• Worksheet