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Ch. 10.5 Regular Polygons
Polygon – Closed plane figure formed from three or more
segments, each of which intersect exactly two
other segments at their endpoints.
Polygons
Not Polygons
Types of polygons
Convex polygon
Concave polygon
All angles open in
At least on angle opens out
Regular Polygon – A polygon whose sides are congruent and
A
angles are congruent.
)
60
Every regular polygon has a center.
Center: point D
D
60
A
60
C
G
The center is equidistant
(same distance) from each
side and vertex.
F
D
DG = DF = DE
C
E
B
DC = DB = DA
B
A
H
I
L
D
K
J
B
C
A
B
A
E
B
F
C
G
F
D
E
C
D
Apothem - Segment drawn from the center of a regular
polygon  (perpendicular) to a side.
A
A
B
E
F
D
C
B
C
D
1) Find the area of ABC 2) Find the area of ABCDEF
A
A
B
24 in
18 cm
G
F
D
5.19
C
20.8
B
E
E
DE = 5.19 cm
A = 140.13
C
H
D
GH = 20.8
cm2
A = 1497.6 in2
Perimeter of a regular polygon
p  ns
perimeter  number of sides  length of a side
Area of a regular polygon
1
A  ap
2
1
Area   apothem  perimeter
2
1) Find the area of a regular triangle if the apothem is 9 in
and each side measures 31.2 in.
A = 421.2 in2
2) Find the area of a regular pentagon if the apothem is
13.8 cm and each side measures 20 cm.
A = 690 cm2
3) If each side of a regular nonagon measures 32 ft and the
apothem is 44 ft, what is the area?
A = 6336 ft2
4) What is the area of a regular 12-gon if each side is 10.2 ft
and the apothem is 19 ft?
A = 1162.8 ft2
5) The area of a regular polygon is 1039.2 ft2. If each side
is 20 ft and the apothem is 17.32 ft, how many sides does
the polygon have?
sides = 6
6) Find the length of the apothem of a regular pentagon if
each side measures 23.2 cm and the area is 928 cm2.
apothem = 16
7) The area of a regular octagon is 4344 in2. Find the length
of each side if the apothem is 36.2 in.
side = 30