The Polygon

Polygon is a closed plane figure bounded by straight lines. There are two basic types of polygons, a convex and a concave polygon. Polygon is said to be convex if no side when extended will pass inside the polygon, otherwise it is concave.
 

concave-and-convex-polygons.jpg

 

Name of Polygons

No. of Sides, n Name
1 Monogon, Henagon (cannot exist)
2 Digon (cannot exist)
3 Triangle, Trigon
4 Quadrilateral, Quadrangle, Tetragon
5 Pentagon
6 Hexagon
7 Heptagon, Septagon
8 Octagon
9 Nonagon, Enneagon
10 Decagon
11 Undecagon, Hendecagon
12 Dodecagon, Duodecagon
13 Tridecagon, Triskaidecagon
14 Tetradecagon, Tetrakaidecagon
15 Pentadecagon, Quindecagon, Pentakaidecagon
16 Hexadecagon, Hexakaidecagon
17 Heptadecagon, Heptakaidecagon
18 Octadecagon, Octakaidecagon
19 Enneadecagon, Ennekaidecagon, Nonadecagon
20 Icosagon
30 Triacontagon
40 Tetracontagon
50 Pentacontagon
70 Heptacontagon
80 Octacontagon
90 Enneacontagon
100 Hectogon
1000 Chilliagon
10 000 Myriagon
1 000 000 Megagon

 

The following are true for convex polygon

  1. The sum of the angles of polygon of n sides is 180°(n - 2) right angles.
  2. The exterior angles of a polygon are together equal to 4 right angles.
Exterior and Interior Angles of Convex Polygon

 

Formulas for convex polygon

Sum of interior angles
$\Sigma \beta = 180^\circ (n - 2)$

 

Sum of exterior angles
$\Sigma \alpha = 360^\circ$

 

Number of Diagonals
$D = \dfrac{n}{2}(n - 3)$

 

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