Polygon Properties

What is a Polygon?

A closed, 2-dimensional figure with three or more straight line segments connected. It is a closed plane figure where line segments are joined together. Though the sides do not cross each other but they meet at every vertex. Circles, quadrilaterals and pentagons are all examples of polygons but circle is not a polygon as it is not joined by any straight line.

Types of polygons

Different kinds of polygons differ on the basis length of sides and size of angles. Some of the different types of polygons are:

Regular polygons: All angles are equal and are of same length. Regular polygons are equiangular as well as equilateral.

Equiangular: In case of equiangular polygon, all angles are equal.

Equilateral: In case of equilateral polygon, all sides are equal.

Convex: When a straight line is drawn through a convex polygon, it crosses over to two sides at the most. However, the interior angles formed are always less than 180 degrees.

Concave: A concave polygon shows somewhat different characteristics as if you draw a straight line through the concave polygon that crosses more than two sides then at least one of the interior angles must be more than 180 degrees.

Different formulas regarding polygons

There are formulas to determine the area of a regular polygon. If you consider N as the number of sides and S as the length from center to a corner then:

Area of a regular polygon = (1/2) N sin(360°/N) S2

Another formula to calculate the sum of the interior angles of a polygon = (N – 2) x 180°.

There are also some formulas to calculate the number of diagonals in a polygon. The formula to calculate the number of diagonals is 1/2 N(N-3)

The number of triangles to be created in a polygon is also derived by the formula (N – 2)

Different terms related to polygons

Diagonal: The diagonal is the line that connects two vertices. However, diagonals are not sides of a polygon.

Exterior Angle: When two adjacent sides form an angle outside the polygon then it is called an exterior angle.

Interior Angle: When two adjacent sides form an angle inside the polygon, then it is called an interior angle.

Side: The lines that make the polygon are called sides.

Vertex: Vertex is the common point where two sides of a polygon meet. The plural of vertex is vertices.

Special types of polygons

There are also some special types of polygons which includes the special quadrilaterals and the special triangles. The list of special quadrilaterals includes polygons like rhombus, parallelogram, square, rectangle and the trapezoid. The list of special triangles includes right, equilateral, scalene, isosceles, obtuse and acute triangles. Each polygon bears a special name according to the number of sides. The following table will let you know of the names of different polygons based on their sides:

Name Sides
N-gon n
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Decagon 10
Dodecagon 12

Some of the other names which have been proposed are:

Name Sides
Nonagon, Enneagon 9
Undecagon, Hendecagon 11
Tridecagon, Triskaidecagon 13
Tetradecagon, Tetrakaidecagon 14
Pentadecagon, Pentakaidecagon 15
Hexadecagon, Hexakaidecagon 16
Heptadecagon, Heptakaidecagon 17
Octadecagon, Octakaidecagon 18
Enneadecagon, Enneakaidecagon 19
Icosagon 20
Triacontagon 30
Tetracontagon 40
Pentacontagon 50
Hexacontagon 60
Heptacontagon 70
Octacontagon 80
Enneacontagon 90
Hectogon, Hecatontagon 100
Chiliagon 1,000
Myriagon 10,000

Further, if you want to name a polygon with number of sides like 86 or 73, then try to follow these rules. You can combine the prefixes and suffixes mentioned below to name polygons with different number of sides.

Thus, an 86 sided Polygon would be called Octacontakaihexagon and a 73 sided polygon would be called Heptacontakaitrigon. However, most people prefer to use the naming format “n-gon” so a 86 sided polygon can be simply called 86-gon.