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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
Quadrilateral or quadrangle
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
11
Undecagon
12
Dodecagon
13
Tridecagon
14
Tetradecagon
Figure 1
Figure 2
Figure 3
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15
Pentadecagon or Quindecagon
16
Hexadecagon
17
Heptadecagon
18
Octadecagon
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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