Polygon- a two dimensional shape formed by connecting three or more line segments at verticies. The term originates from "poly" the Greek meaning of many, and "gon" from "gonia" the meaning of a closed figure.

Convex Polygon- a polygon with all interior angles less than 180 degrees, all diagonals drawn from any vertex remain within the polygon

- a polygon with no part of any line segment (diagonal) joining two verticies outside the polygon

Concave Polygon - a polygon with one or more interior angles greater than 180 degrees, some diagonals drawn from a vertex will pass outside the polygon

- a polygon with parts of some line segments (diagonals) joining two verticies on the polygon outside the polygon

Regular Polygon - a polygon with all side lengths equal and all interior angles equal, also termed as equilateral and equiangular. (ie. square, equilateral triangle)

Examples of Convex and Concave Polygons

Examples of Regular Polygons

(For more names of polygons refer to the chart at the bottom of the page)

Any polygon can be seperated into triangles, which leads to the equations of polygons

EquationsThe formula for determining the sum of the interior angles of a polygon in degrees

There is no formula for determining the sum of a polygon's exterior angles - all regular polygon's exterior angles have a sum of 360

But for finding each of the exterior angles one can just divide the exterior angle total by the number of sides or take one angle and use supplementay angles to subtract the interior angle by 180°

Example 1: 360/12=30 Example 2: Given interior angle is 150°

180 - 150 = 30

Examples

a)find the sum of the interior angles of a dodecagon (12 sided polygon)

sum= 180(n-2)
=180(12-2)
=180(10)
=1800°

b) how many sides would a polygon have all of its interior angles measured 140° ?
sum= 180°
140n=180(n-2)
140n=180n-360
140n-180n=-360
-40/-40 = -360/-40
n=9

c)a regular polygon has 5 sides, find the measures of each interior angle.
sum= 180(n-2)
= 180(5-2)
= 180(3)
= 540°

each= 540/5
= 108°

Naming Polygons

Name

Edges

Interior Angles

Name

Edges

Interior Angles

Henagon

1

-360°

Dodecagon

12

1800°

Digon

2

0°

Tridecagon/ Triskaidecagon

13

1980°

Triangle/ Trigon

3

180°

Tetradecagon/ Tetrakaidecagon

14

2160°

Quadrilateral /Tetragon

4

360°

Pentdecagon

15

2340°

Pentagon

5

540°

Hexdecagon

16

2520°

Hexagon

6

720°

Heptadecagon

17

2700°

Heptagon

7

900°

Octadecagon

18

2880°

Octagon

8

1080°

Nonadecagon/ Ennedecagon

19

3060°

Nonagon/
Enneagon

9

1260°

Icosagon

20

3240°

Decagon

10

1440°

Chiliagon

1 000

179640°

Hendecagon

11

1620°

Megagon

1 000 000

179999640°

Angles though not truely apart of polygons is valid but is from the Angles section. Click on the Link to see angles after finishing this page.

History of the Polygon

Polygons were descovered in ancient times by the greeks. In 1796, Gause descovered the first 17 sided regular polygon when he was only 18 years old.From then, people all over the world have been finding many different types of polygons. Even historiens have found polygon shapes on ancient artifacts. The most recent discovery of polygons is on mars, scientists have found polgyon like shapes on the surface of the planet.

Works Cited:

Hendriks, J., MPM 1D1, (2009). / Knill, G. ET ALL(1999). Math Power 9 . /Google Images. (2009). / Knill, G. ET ALL(1993). Math Power 9 .

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DefinitionsPolygon- a two dimensional shape formed by connecting three or more line segments at verticies. The term originates from "poly" the Greek meaning of many, and "gon" from "gonia" the meaning of a closed figure.Convex Polygon- a polygon with all interior angles less than 180 degrees, all diagonals drawn from any vertex remain within the polygon## - a polygon with no part of any line segment (diagonal) joining two verticies outside the polygon

Concave Polygon- a polygon with one or more interior angles greater than 180 degrees, some diagonals drawn from a vertex will pass outside the polygon## - a polygon with parts of some line segments (diagonals) joining two verticies on the polygon outside the polygon

Regular Polygon- a polygon with all side lengths equal and all interior angles equal, also termed as equilateral and equiangular. (ie. square, equilateral triangle)## (For more names of polygons refer to the chart at the bottom of the page)

## Any polygon can be seperated into triangles, which leads to the equations of polygons

The formula for determining the sum of the interior angles of a polygon in degreesEquationsnrepresents the number of sides## Sum=180(

n-2)## There is no formula for determining the sum of a polygon's exterior angles - all regular polygon's exterior angles have a sum of 360

But for finding each of the exterior angles one can just divide the exterior angle total by the number of sides or take one angle and use supplementay angles to subtract the interior angle by 180°

## Example 1: 360/12=30 Example 2: Given interior angle is 150°

## 180 - 150 = 30

Examplesa)find the sum of the interior angles of a dodecagon (12 sided polygon)sum= 180(n-2)

=180(12-2)

=180(10)

=1800

°b)how many sides would a polygon have all of its interior angles measured 140° ?sum= 180°

140n=180(n-2)

140n=180n-360

140n-180n=-360

-40/-40 = -360/-40

n=9

c)a regular polygon has 5 sides, find the measures of each interior angle.sum= 180(n-2)

= 180(5-2)

= 180(3)

= 540

°each= 540/5

= 108

°Naming PolygonsTriskaidecagon

Trigon

Tetrakaidecagon

/Tetragon

Ennedecagon

Enneagon

Angles though not truely apart of polygons is valid but is from theAngles section. Click on the Link to see angles after finishing this page.

Polygons were descovered in ancient times by the greeks. In 1796, Gause descovered the first 17 sided regular polygon when he was only 18 years old.From then, people all over the world have been finding many different types of polygons. Even historiens have found polygon shapes on ancient artifacts. The most recent discovery of polygons is on mars, scientists have found polgyon like shapes on the surface of the planet.History of the PolygonWorks Cited:Hendriks, J., MPM 1D1, (2009). / Knill, G. ET ALL(1999).

Math Power 9./Google Images. (2009). / Knill, G. ET ALL(1993).Math Power 9.