What is an Irregular Polygon? - Definition & Shapes

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  • 0:00 Polygons
  • 0:49 Irregular Polygons
  • 1:27 N-Sided Regular and…
  • 3:06 Example
  • 3:57 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

Polygons show up often in the world around us. This lesson will define regular and irregular polygons and teach us to distinguish between the two. We will become familiar with different n-sided polygons and their shapes.

Polygons

Did you know that when you are writing on a piece of paper, you are writing on a polygon, or that when you are looking at certain street signs, you are looking at a polygon? A polygon is a two-dimensional shape with at least three sides that are straight and create interior angles where they meet. They show up all the time in the world around us.

Polygons can be regular or irregular. In order to define an irregular polygon, we must first look at regular polygons. A regular polygon is a polygon with all sides of equal length and all interior angles of equal measure. For example, a yield street sign is a regular polygon with three sides.

Now that we understand what a regular polygon is, we can move on to what this lesson is all about: irregular polygons.

Irregular Polygons

An irregular polygon is a polygon that is not regular. That is, an irregular polygon is a polygon that does not have all sides of equal lengths and all interior angles equal. For example, consider this picture of an SD card:

5-sided Irregular Polygon
irregular3

Notice the SD card has 5 sides and they are not all equal length. Also, the interior angles are not all equal. Therefore, the SD card takes on the shape of an irregular polygon.

These are all things that you may come across on a daily basis. Isn't it neat how mathematics can make us look at the world around us so differently when we learn something new?

N-Sided Regular and Irregular Polygons

Notice that the polygons that we've given examples of all have a different number of sides. Polygons can have any number of sides as long as there are three or more of them. A lot of n-sided polygons have special names. For example, a piece of paper has four sides, and we call it a quadrilateral. The yield sign has three sides, and we call it a triangle. Lastly, the SD card has five sides, and we call it a pentagon.

The special names we give polygons with certain numbers of sides can either be regular or irregular. For instance, the yield sign was a regular polygon with three sides. As we said, a polygon with three sides is called a triangle. Thus, we would call the yield sign a regular triangle. Similarly, the SD card is called a pentagon because it has five sides. Since it is irregular, we would call it an irregular pentagon.

Let's go through some other kinds of polygons with special names. So, the first one we already know. A polygon with three sides is a triangle. A polygon with four sides is called a quadrilateral and one with five sides, we already know that's a pentagon. A polygon with six sides is referred to as a hexagon, one with seven sides is called a heptagon, and, finally, a polygon with eight sides is an octagon.

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