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POLYGONS
1.1. Definition
Polygon is derived from two Greek words, “poly” meaning many and “goniameaning angle. It
is a closed plane bounded by line segments as the sides and with three or more angles.
A convex polygon, as seen in Fig. 1, is a polygon with each interior angle less than 180
while a concave polygon (Fig. 2) is a polygon having one or more angles greater than 180.
A regular polygon is a polygon with all sides and interior angles equal (Fig. 3), otherwise,
it is an irregular polygon. Both Fig. 1 and Fig. 2 are examples of irregular polygons.
1.2. Names of polygons according to number of sides
NUMBER OF SIDES
NAME
3
Triangle
4
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
11
Undecagon
12
Dodecagon
13
Tridecagon
14
Figure 1
Figure 2
Figure 3
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15
16
17
18
19
Nondecagon
20
Icosagon
30
Triacontagon
40
Tetracontagon
50
Pentacontagon
60
Hexacontagon
70
Heptacontagon
80
Octacontagon
90
Enneacontagon
100
Hectagon
1000
Chillagon
10,000
Myriagon
Prefixes
Icosakai (20+_)
Triacontakai (30+_)
Tetracontakai (40+_)
Pentacontakai (50+_)
Hexacontakai (60+_)
Heptacontakai (70+_)
Octacontakai (80+_)
Ennecontakai (90+_)
Suffixes
Henagon (1)
Digon (2)
Trigon (3)
Tetragon (4)
Pentagon (5)
Hexagon (6)
Heptagon (7)
Octagon (8)
Enneagon (9)
Examples: 23 sides = icosakaitrigon, 45 sides = tetracontakaipentagon,
67 sides = hexacontakaiheptagon, 59 sides = pentacontakaienneagon,
81 sides = octacontakaihenagon
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1.3. Parts of a Polygon
a. Vertex intersection of the sides
b. Interior angle the angle inside the polygon bounded by two adjacent sides Sum of
all interior angles
 󰇛 󰇜
where n = number of sides of the polygon
Measurement of each interior angle

󰇛󰇜
c. Exterior angle the angle formed by the prolongation of one side to the adjacent side
Sum of all exterior angle = 360
Measurement of each exterior angle


d. Diagonal is a line segment connecting two non-adjacent vertices Number of
diagonals in a polygon
󰇛󰇜
Fig
4
Internal angle, Ꝋ
i
Dia
gonal
Vertex
External
angle, Ꝋ
e
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Example:
1. Given a 14 sided polygon.
a. Compute the sum of its interior angles.
b. Compute the number of diagonals of the polygon.
c. If it’s a regular polygon, what is the measure of each exterior angle?
Solution:
a) 󰇛 󰇜
󰇛 󰇜

b)
󰇛󰇜
󰇛 󰇜

c) 




 

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