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PROJECT
IN
MATH
Submitted to:
Ms. Mila Novabos
Submitted by:
Christine Joy Y. Antoque
III – Putian
POLYGONS
Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed"
(all the lines connect up).
Not a Polygon
(has a curve)
Polygon
(straight sides)
Not a Polygon
(open, not closed)
Polygon comes from Greek. Poly- means "many" and -gon means "angle".
Types of Polygons
Regular or Irregular
If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular
Regular
Irregular
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more
than 180°.
If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a
"cave" in it)
Convex
Concave
Simple or Complex
A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon
intersects itself! Many rules about polygons don't work when it is complex.
Simple Polygon
(this one's a Pentagon)
Complex Polygon
(also a Pentagon)
More Examples
Irregular Hexagon
Concave Octagon
Complex Polygon
(a "star polygon",
in this case a pentagram)
Names of Polygons
If it is a Regular Polygon...
Shape
Interior Angle
Name
Sides
Triangle (or Trigon)
3
60°
Quadrilateral (or Tetragon)
4
90°
Pentagon
5
108°
Hexagon
6
120°
Heptagon (or Septagon)
7
128.571°
Octagon
8
135°
Nonagon (or Enneagon)
9
140°
Decagon
10
144°
Hendecagon (or Undecagon)
11
147.273°
Dodecagon
12
150°
Triskaidecagon
Tetrakaidecagon
Pentadecagon
Hexakaidecagon
Heptadecagon
Octakaidecagon
Enneadecagon
Icosagon
Triacontagon
Tetracontagon
Pentacontagon
Hexacontagon
Heptacontagon
Octacontagon
13
14
15
16
17
18
19
20
30
40
50
60
70
80
152.308°
154.286°
156°
157.5°
158.824°
160°
161.053°
162°
168°
171°
172.8°
174°
174.857°
175.5°
Enneacontagon
Hectagon
Chiliagon
Myriagon
Megagon
Googolgon
90
100
1,000
10,000
1,000,000
10100
176°
176.4°
179.64°
179.964°
~180°
~180°
n-gon
n
(n-2) × 180° / n
You can make names using this method:
Start with...
Sides
Sides ...end with
Icosi...
20
+1 ...henagon
Triaconta...
30
+2 ...digon
Tetraconta...
40
+3 ...trigon
Pentaconta...
50
+4 ...tetragon
Hexaconta...
60
+5 ...pentagon
70 Heptaconta...
+6 ...hexagon
Octaconta...
80
+7 ...heptagon
90 Enneaconta...
+8 ...octagon
Hecta...
100
+9 ...enneagon
etc..
Example: a 62-sided polygon is a Hexacontadigon
BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-gon" ...
"100-gon", etc.