Areas of Regular Polygons

1
Areas of Regular Polygons

• The apothem of a regular polygon is a
  perpendicular segment from the center of the
  polygon to any side of the polygon
• The length of this segment is also called the
  apothem
• The center of the regular polygon is also the
  center of a circle circumscribed about the
  polygon
• The area of a regular polygon can be computed by
  breaking it up into isosceles triangles and
  adding up the areas of the triangles
• Each triangle has a base equal to the length s of
  a side of the polygon, and a height equal to the
  length a of the apothem

Opossum
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Areas of Regular Polygons

• Investigation
• Area Formula for Regular Polygons
• Step 1 Find the area of one isosceles triangle
  in terms of a and s.
• Step 2 Use this result to find the area of the
  regular pentagon.
• Step 3 Repeat steps 1 and 2 and complete the
  table below.
• C-80 Regular Polygon Area Conjecture
• The area of a regular polygon is given by the
  formula A ½nsa, where A is the area, n is the
  number of sides, s is the length of each side,
  and a is the apothem.
• The perimeter, P, is the number of sides times
  the length of each side, or P ns. This gives
  an alternative formula for area of a regular
  polygon, A ½Pa