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Polygons - Classification

regular circle interior angles

A regular polygon is one whose whose sides and interior angles are congruent. Regular polygons can be inscribed by a circle such that the circle is tangent to the sides at the centers, and circumscribed by a circle such that the sides form chords of the circle. Regular polygons are named to indicate the number of their sides or number of vertices present in the figure. Thus, a hexagon has six sides, while a decagon has ten sides. Examples of regular polygons also include the familiar square and octagon.

Not all polygons are regular or symmetric. Polygons for which all interior angles are less than 180° are called Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Name of the polygon Number of sides in polygon Number of vertices of polygon
Triangle 3 3
Rectangle 4 4
Pentagon 5 5
Hexagon 6 6
Heptagon 7 7
Octagon 8 8
Nonagon 9 9
Decagon 10 10
n-gon n n

convex. Polygons with one or more interior angles greater than 180° are called concave.

The most common image of a polygon is of a multisided perimeter enclosing a single, uninterrupted area. In reality, the sides of a polygon can intersect to form multiple, distinct areas. Such a polygon is classified as reflex.

Polygons - Angles [next]

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