Area and Perimeter: Areas of Regular Polygons

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Area and PerimeterAreas of Regular Polygons
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Review Inscribed Polygons Circumscribed
Circles
Inscribed means written inside
Circumscribed means written around (the outside)
Def A polygon is inscribed in a circle the
circle is circumscribed about the polygon when
each vertex of the polygon lies on the circle.
Def A ________________is a polygon that is
equiangular equilateral.
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Inscribed Regular Polygons Triangles
Inscribed Regular Pentagon
Total of Interior Angles ___________ Each
Interior Angle ______________
5 congruent isosceles triangles Total of Central
Angles _________ Each central angle
_____________
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Parts of a Regular Polygon

• A stands for Area
• A(nonagon) is the area of a regular 9-sided
  figure.
• n is the number of sides of a regular polygon
• p is perimeter, r is radius, s is side
• a is apothem
• ____________ The line segment from the center
  of a regular polygon to the midpoint of a side or
  the length of this segment.
• Sometimes known as the ______________, or the
  radius of a regular polygons inscribed circle.

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Regular Polygon Area Theorem
Given an inscribed regular n-gon (shown as an
octagon)
A(n-gon)
Regular Polygon Area Theorem The area of a
regular polygon is _______________________________
____________ _____________________________________
_______________
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Regular Polygon Terminology
_______________________- the center of the
circumscribed circle (O).
_______________________- the distance from the
center to a vertex (OX).
_____________________________- an angle formed by
2 radii drawn to consecutive vertices. (
)
____________________________- the (perpendicular)
distance from the center of the polygon to a
side. (OM)
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Example Square
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Example Equilateral Triangle
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Example Regular Hexagon
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Regular Nonagon
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Examples
r
r
a
a
r a A
1.
2. 8 5
3. 49
4.
r a p A
5. 6
6. 4
7. 12
8.
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More Examples
s
r
r
r
a
a
a
x
x
x
1. r , find A. 2. a 6, find A.
3. a 8, find p. 4. r 12, find s.
5. s 8, find r.