9'4 Areas of Regular Polygons

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9.4 Areas of Regular Polygons

• February 6, 2008

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Definitions (associated with regular polygons
only)

• Center of a polygon the center of its
  circumscribed circle.
• Radius of a polygon the radius of its
  circumscribed circle, or the distance from the
  center to a vertex.
• Apothem of a polygon distance from the center
  to any side of the polygon.

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• The center of circle A is
• A
• The center of pentagon BCDEF is
• A
• A radius of circle A is
• AF
• A radius of pentagon BCDEF is
• AF
• An apothem of pentagon BCDEF is
• AG

B
C
F
A
G
E
D
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Area of a regular polygon

• The area of a regular polygon is
• A ½ Pa
• Area
• Perimeter apothem

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Where does the equation come from?

F

• The apothem is the height of a triangle between
  the center and two consecutive vertices of the
  polygon.
• you can find the area o any regular n-gon by
  dividing the polygon into congruent triangles.

A
H
a
E
G
B
D
C
Hexagon ABCDEF with center G, radius GA, and
apothem GH
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Ex 1 A regular octagon has an apothem of 4
in. Side length is 3. Find its area.
Step 1 Find Perimeter 3 x 8 24 Step 2 Use
Equation
a
4
A ½ Pa
½ (24)(4)
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Ex. 2 Finding the area of a regular polygon

• A regular pentagon is inscribed in a circle with
  a side length of 7.5 and an apothem of 5.2. Find
  the area of the pentagon.

C
B
D
A