Skip to main content
Search IntMath

Determining if a Plane Figure Can Be Regular

By Kathleen Cantor, 10 Sep 2020

Faced with the task of teaching your kids the geometry you learned in school, but no longer remember? Panicking because you can't remember a simple phone number anymore, let alone mathematical theories? Fell asleep during your Zoom math class? You're not alone.

COVID-19 has everyone hunkered down at home, and "school teacher" has been added to our parental responsibilities. We've all been scrambling to remember the math lessons we learned long ago, worried that the methods we were taught in school won't translate into today's new math standards. Fortunately, some things remain the same, including elements of basic geometry.

If you need to determine whether or not a plane figure is regular, here is your refresher course.


First of all, let's break down the terminology. Once you understand the terms, answering the question won't be so hard.

  • Plane: A plane is any flat surface, your floors, the ceiling of a room, your cell phone screen.
  • Plane Figure: Any shape that is flat and closed-in by lines, is a plane figure. It can have straight or curvy lines: a circle, a star, triangles, or crescents.
  • Regular Plane Figure: A regular plane figure is a plane figure whose sides and interior angles are all the same. A square is a regular plane figure; so is a circle.

Now that you know the terms, it doesn't feel quite so challenging, does it? Don't worry. It doesn't get harder!

Regular or Not?

How do you determine if a plane figure is regular? It's simple. Take your ruler and protractor and measure all of the sides and all of the interior angles. If all of the sides are the same, and all of the interior angles are the same, it's regular!


Let's practice. Determining if a plane figure is regular can be done with any object. Grab some everyday objects from around your house.

Cell Phone Screen:

Top & Bottom: 2.5 inches

Sides: 4 inches

Determination: Not Regular.

You don't even have to check the interior angles, because the sides are not all the same length.

Pizza Box:

Sides: 13 inches each

Interior Angles: 90 degrees each

Determination: Regular.

Each side is the same length: 13 inches. All four of the interior angles are 90 degrees.

Tortilla Chip:

Left side: 2 inches

Right Side: 2.5 inches

Bottom: 3.5 inches

Determination: Not Regular.

Again, you don't even have to check the interior angles, because the sides are not the same length. Sadly, when I ate my chip, I also determined it was stale.

Dinner Plate:

Sides: Because a dinner plate is a circle, it only has one side. You do not have to measure it in this case.

Angles: Again, being a circle, it only has one angle. Circles share a universal angle: 360 degrees.

Determination: Regular.

Technically a circle only has one "side" and one interior angle. It qualifies as a regular plane figure.

You Can Do This

Bottom line: don't be intimidated. You can do this. We use geometry every day without even realizing it. Most of the time, you can just look at a shape and tell if it's regular or not. Regular plane figures are symmetrical. Your brain recognizes regular plane figures immediately based on that symmetry. It even finds it soothing.

Grab a ruler and a protractor, a random object around the house, and grab your kid. It's time for some geometry! Show them you're a boss when it comes to determining whether or not a plane figure is regular.

Be the first to comment below.

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.