ArEa Of ReGuLaR pOlYgOnS aNd CiRcLeS

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ArEa Of ReGuLaR pOlYgOnS aNd CiRcLeS

• By Tarra Tuttle
• 5th period

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Area of a Regular Polygon
If a regular polygon has an area of A square
units, a perimeter of P units, and an apothem of
a units, then A1/2Pa.
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Example 1
Find the area of a regular polygon that has a
perimeter of 72 in.
F
G
E
H
O
D
A
P
B
C
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Area of a Circle
If a circle has an area of A square units and a
radius of r units, then Ap r
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Example 2a
The area of a circular pool is approximately
7850 square feet. The owner wants to replace the
tilling at the edge of the pool.
6 inches
He plans to use tiles that are each 6-inch
squares since the edging is 6 inches wide. How
many tiles should he purchase?
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Example 2b
Once the square tiles are place around the
circular pool, there will be extra space between
each square. What shape of tile will fill this
space and how many tiles of this shape will he
need to go around the pool?
The best shape would be a triangle. The owner
will need the same number of triangular tiles as
6-in square tiles.
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Example 3
Find the area of the shaded region if the measure
of and BCA equals 60.
Ap r
Triangle AOR is a 30-60-90 triangle, so OR4 and
AR 4 3. Since AC 2(AR) AC 2(4 3) or 8 3. the
perimeter of triangle ABC is 3(8 3) or 24 3.
A p (8)
A 64 p
B
A201.1
O
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A ½ Pa 1/2 (24 3)(4)
201.1- 83.1118.0 square units.
A
R
C
A83.1
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!!!ThE eNd!!!!