9.4 Areas of Regular Polygons

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9.4 Areas of Regular Polygons

• Geometry CP
• Chapter 9 Area

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Investigation

• Take a regular polygon of n sides

• Divide it into n congruent isosceles triangles
  by drawing radii from the center of the
  circumscribed circle to each vertex of the polygon

• You can find the area of one isosceles triangles
  and multiply by the number of isosceles triangles
  in the polygon (which is n) to find the area of
  the polygon

?
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Definition

• An apothem of a regular polygon is a
  perpendicular segment from the center of the
  polygons circumscribed circle to a side of the
  polygon

apothem
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Find the Area
1 2

• A (b)(h) x ( of triangles)

b side of polygon s h height of triangle
apothem a n sides
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Area of Regular Polygon
Since the perimeter length of each side times
the number of sides, or p sn, then the formula
can be written
1 2
A a p
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Examples

1. Hexagon a 4 cm and s 5 cm

2. Octagon a 3 in and s 7 in
3. Heptagon a 10 cm and p 75 cm
(7 sides)
4. Dodecagon p 95cm and a 8cm
(12 sides)
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Homework

• Page 452
• 1-4, 8-10