Is a Pentagon a Regular Polygon?

Instructor: Joy Blake

Joy has been a teacher for over ten years. She has primarily taught Middle School Math and has a Master's degree in Educational Leadership.

Math involves not just numbers, but also shapes. In this lesson, we will look at the two types of polygons, regular and irregular, and use that information to figure out what type of polygon a pentagon is.

What is a Pentagon?

Today in class Cheyenne is learning about a shape called a pentagon. She recognizes the shape immediately because she has drawn it every time she draws a house. She didn't even realize that she was actually drawing a pentagon.

A pentagon is a shape with five straight sides and five angles. The angles within a pentagon add up to 540 degrees.

This pentagon is a regular polygon with 5 equal sides and 5 equal angles
yellow pentagon

The prefix penta means five and the suffix gon means angles. So, when you put it all together, a pentagon has to have five angles. It is a five sided shape with five angles.

Now that Cheyenne knows what a pentagon is, her teacher wants her to take it to another level and figure out if a pentagon is a regular polygon. Before she can do that, she must first figure out what a polygon is.

What is a Polygon?

The prefix poly means many and you just learned that gon means angles, so, putting them together, a polygon is a shape with many angles. Every shape that has sides is considered to be a polygon.

All polygons share some things in common: they are shapes that have angles and closed, straight sides. What closed means is that all of the sides must meet - if one side does not meet with another side, then it would be open, and not a polygon.

All polygons then fall into two categories. They are either regular polygons or irregular polygons.

Regular vs. Irregular

Regular polygons are equiangular and equilateral. The prefix equi means equal, the suffix angular means angle, and the suffix lateral means side. So, this means that regular polygons have equal angles and equal sides.

An irregular polygon does not have equal angles and sides.

Irregular polygons have different measurements for their sides and angles
irregular polygon

What Type of Polygon Is a Pentagon?

Well, let's go back to Cheyenne. She has already learned a lot about a pentagon. She has learned that:

  • a pentagon has five sides
  • a pentagon has five angles
  • a pentagon is a closed shape

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