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Polygon Classification

Categories of polygons based on the number of sides.

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Polygon Classification

What if you were told how many sides a polygon has? How would you describe the polygon based on that information? After completing this Concept, you'll be able to classify a polygon according to its shape and the number of sides it has.

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CK-12 Classifying a Polygon

James Sousa: Introduction to Polygons

Then watch the first part of this video.

James Sousa: Classifying Polygons


A polygon is any closed, 2-dimensional figure that is made entirely of line segments that intersect at their endpoints. Polygons can have any number of sides and angles, but the sides can never be curved. The segments are called the sides of the polygons, and the points where the segments intersect are called vertices .


A convex polygon does not cave in. Convex polygons look like:

A diagonal is a non-side line segment that connects two vertices of a convex polygon.

The red line segments are all diagonals. This pentagon has 5 diagonals.

Whether a polygon is convex or concave, it is always named by the number of sides. Explore the relationship between the number of sides of a convex polygon and its diagonals. Can you complete the table?

Polygon Name Number of Sides Number of Diagonals Convex Example
Triangle 3 0
Quadrilateral 4 2
Pentagon 5 5
Hexagon 6 9
Heptagon 7 ?
Octagon 8 ?
Nonagon 9 ?
Decagon 10 ?
Undecagon or hendecagon 11 ?
Dodecagon 12 ?
n-gon n (where n > 12 ) ?

Example A

Which of the figures below is a polygon?


Example B

Determine if the shapes below are convex or concave.


Example C


The pink polygon is a concave hexagon (6 sides).

The green polygon convex pentagon (5 sides).

The yellow polygon is a convex decagon (10 sides).

CK-12 Classifying a Polygon

Guided Practice

1. Which of the figures below is not a polygon?

2. How many diagonals does a 7-sided polygon have?

3. True or false: A quadrilateral is always a square.



2. Draw a 7-sided polygon, also called a heptagon.


3. False. Only quadrilaterals with four congruent sides and four right angles will be squares. There are many quadrilaterals (such as rectangles, kites, parallelograms, trapezoids, etc.) that are not necessarily squares.


In problems 1-6, name each polygon in as much detail as possible.

  1. Explain why the following figures are NOT polygons:

For 12-14, determine if the statement is true or false.

  1. A polygon must be enclosed.
  2. A star is a convex polygon.
  3. A 5-point star is a decagon


diagonal (of a polygon)

diagonal (of a polygon)

A non-side line segment that connect two vertices of a convex polygon.


A polygon is a simple closed figure with at least three straight sides.


A concave polygon has at least one interior angle greater than 180 degrees. A common way to identify a concave polygon is to look for a "caved-in" side of the polygon.


A convex polygon contains no interior angles greater than 180 degrees.


Exterior angles

Exterior angles

An exterior angle is the angle formed by one side of a polygon and the extension of the adjacent side.
Interior angles

Interior angles

Interior angles are the angles inside a figure.
Regular Polygon

Regular Polygon

A regular polygon is a polygon with all sides the same length and all angles the same measure.


Vertices are points where line segments intersect.


A polygon is equilateral if all of its sides are the same length.

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