Areas of Regular Polygons

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Section 11-2

• Areas of Regular Polygons

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Area of an Equilateral Triangle

• The area of an equilateral triangle is one fourth
  the square of the length of the side times

Formula
or
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Given any regular polygon, you can circumscribe a
circle about it.
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Parts of a Regular Polygon
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Center

• is the center of the circumscribed circle

Example
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Radius

• is the distance from the center to a vertex

Example
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apothem

• is the (perpendicular) distance from the center
  of the polygon to a side.

Example
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Central angle

• is an angle formed by two radii drawn to
  consecutive vertices.

Example
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To find the Measure of a Central Angle of a
Regular Polygon
n the number of sides
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To find the area of any regular n-gon

• Divide the polygon into congruent triangles
• Find the area of one of those triangles
• Multiply that triangles area by the number of
  triangles that are in the polygon

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Area of a regular polygon

• The area of a regular polygon is equal to half
  the product of the perimeter and the apothem.

Formula