# Geometry/Polygon

A **Polygon** is a two-dimensional figure, meaning all of the lines in the figure are contained within one plane. They are classified by the number of angles, which is also the number of sides.

One key point to note is that a polygon must have at least three sides. Normally, three to ten sided figures are referred to by their names (below), while figures with eleven or more sides is an *n*-gon, where *n* is the number of sides. Hence a forty-sided polygon is called a 40-gon.

A polygon with three angles and sides.

A polygon with four angles and sides.

*Pentagon*

A polygon with five angles and sides.

*Hexagon*

A polygon with six angles and sides.

*Heptagon*

A polygon with seven angles and sides.

*Octogon*

A polygon with eight angles and sides.

*Nonagon*

A polygon with nine angles and sides.

*Decagon*

A polygon with ten angles and sides.

For a list of n-gon names, go to [1] and scroll to the bottom of the page.

Polygons are also classified as **convex** or **concave**. A convex polygon has interior angles less than 180 degrees, thus all triangles are convex. If a polygon has at least one internal angle greater than 180 degrees, then it is concave. An easy way to tell if a polygon is concave is if one side can be extended and crosses the interior of the polygon. Concave polygons can be divided into several convex polygons by drawing diagonals. **Regular polygons** are polygons in which all sides and angles are congruent.