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What is a Polygon?
A closed plane figure made up of several line segments that are joined
together. The sides do not cross each other. Exactly two sides meet at
every vertex.
Types |
Formulas | Parts
| Special Polygons | Names
Types of Polygons
Regular - all angles are equal and all sides are the same length.
Regular polygons are both equiangular and equilateral.
Equiangular - all angles are equal.
Equilateral - all sides are the same length.
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Convex - a straight line drawn through a convex polygon crosses
at most two sides. Every interior angle is less than 180°. |
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Concave - you can draw at least one straight line through
a concave polygon that crosses more than two sides.
At least one interior angle is more than 180°. |
Polygon Formulas
(N = # of sides and S = length from center to a corner)
Area of a regular polygon = (1/2) N sin(360°/N) S2
Sum of the interior angles of a polygon = (N - 2) x 180°
The number of diagonals in a polygon = 1/2 N(N-3)
The number of triangles (when you draw all the diagonals from one
vertex) in a polygon = (N - 2)
Polygon Parts
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Side - one of the line segments
that make up the polygon.
Vertex - point where two sides
meet. Two or more of these points are called vertices.
Diagonal - a line connecting
two vertices that isn't a side.
Interior Angle - Angle formed
by two adjacent sides inside the polygon.
Exterior Angle - Angle formed
by two adjacent sides outside the polygon.
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Special Polygons
Special
Quadrilaterals - square, rhombus, parallelogram, rectangle, and the
trapezoid.
Special
Triangles - right, equilateral, isosceles, scalene, acute, obtuse.
Polygon
Names
Generally accepted names
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Sides
|
Name |
|
n
|
N-gon |
|
3
|
Triangle |
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4
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Quadrilateral |
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5
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Pentagon |
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6
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Hexagon |
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7
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Heptagon |
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8
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Octagon |
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10
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Decagon |
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12
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Dodecagon |
Names for other polygons have been proposed.
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Sides
|
Name |
|
9
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Nonagon, Enneagon |
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11
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Undecagon, Hendecagon |
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13
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Tridecagon, Triskaidecagon |
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14
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Tetradecagon, Tetrakaidecagon |
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15
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Pentadecagon, Pentakaidecagon |
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16
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Hexadecagon, Hexakaidecagon |
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17
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Heptadecagon, Heptakaidecagon |
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18
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Octadecagon, Octakaidecagon |
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19
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Enneadecagon, Enneakaidecagon |
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20
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Icosagon |
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30
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Triacontagon |
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40
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Tetracontagon |
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50
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Pentacontagon |
|
60
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Hexacontagon |
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70
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Heptacontagon |
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80
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Octacontagon |
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90
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Enneacontagon |
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100
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Hectogon, Hecatontagon |
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1,000
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Chiliagon |
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10,000
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Myriagon |
To construct a name, combine the prefix+suffix
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Sides
|
Prefix |
|
20
|
Icosikai... |
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30
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Triacontakai... |
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40
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Tetracontakai... |
|
50
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Pentacontakai... |
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60
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Hexacontakai... |
|
70
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Heptacontakai... |
|
80
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Octacontakai... |
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90
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Enneacontakai... |
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+
|
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Sides
|
Suffix |
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+1
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...henagon |
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+2
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...digon |
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+3
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...trigon |
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+4
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...tetragon |
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+5
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...pentagon |
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+6
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...hexagon |
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+7
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...heptagon |
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+8
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...octagon |
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+9
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...enneagon |
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Examples:
46 sided polygon - Tetracontakaihexagon
28 sided polygon - Icosikaioctagon
However, many people use the form n-gon, as in 46-gon, or 28-gon instead
of these names.
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