Nonagon: Definition & Shape

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  • 0:05 Definition of a Nonagon
  • 0:32 Regular Nonagons
  • 1:40 Irregular Nonagons
  • 2:05 An Example of a Nonagon
  • 2:39 Lesson Summary
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Lesson Transcript
Instructor: Jennie Brady

Jennie has eight years experience teaching high school math and has a Master's degree in Education Leadership.

In this lesson, we are going to learn about regular and irregular nonagons. We will also look at some examples of each and discuss the properties that apply to nonagons.

Definition of a Nonagon

A nonagon is a nine-sided polygon. You may recall that a polygon is a many-sided shape. We use the suffix -gon to indicate the number of sides of a polygon.

Here are some commonly used polygon names:

Name Number of Sides
triangle 3
quadrilateral 4
pentagon 5
hexagon 6
heptagon 7
octagon 8
nonagon 9
decagon 10

Did you see the pattern pick up after the four-sided polygon? Did you know that as the numbers get larger, you can name the polygon by simply putting the number before the suffix? For example, a seventeen-sided shape would be a 17-gon.

Regular Nonagons

A regular polygon is a polygon with equal sides and equal angles. Let's look at quadrilaterals for a moment. There are many different shapes within the category of quadrilaterals; a parallelogram, rectangle, trapezoid, rhombus and square.

Quadrilaterals

You may not realize it, but a square is a regular polygon. More specifically, a square is a regular quadrilateral, or four-sided shape. It has four equal sides and four right angles, each measuring 90 degrees.

Regular Quadrilateral

A regular nonagon is a nine-sided shape with equal sides and equal angles of 140 degrees each.

Regular Nonagon

The length of sides would depend on the exact example you are looking at, but know that all regular nonagons are similar shapes so they have the same angle measures. You can solve for the measure of one interior angle using this formula:

((n - 2) * 180)/n

n = the number of sides

In the case of a nonagon, you would perform the following operation:

Solve for the measure of one interior angle of a regular nonagon
((n - 2) * 180)/n
((9-2) * 180)/9
(7 * 180)/9
1260/9
140

Each interior angle measure of a regular nonagon is 140 degrees.

Irregular Nonagons

An irregular polygon is a polygon with unequal sides and angles. An irregular nonagon is a nine-sided shape that does not have equal sides or angles. One real world example of an irregular nonagon is the US Steel Building in Pittsburgh, Pennsylvania. It looks like a triangle with each corner indented. It might not look like it does at first glance, but this creates a total of nine sides. Go ahead: count them up!

US Steel Building

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