Measuring the Area of Regular Polygons: Formula & Examples

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Measuring the Angles of Triangles: 180 Degrees

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:07 A Regular Polygon
  • 0:46 Sides
  • 1:26 The Apothem
  • 1:53 Finding the Area
  • 3:32 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn why a regular polygon makes your life easier when it comes to finding the area inside one. Learn the one formula for area that will work for any type of regular polygon.

A Regular Polygon

Regular polygons are everywhere! Just look around you, and you will see them, especially when you're driving around. Look at a stop sign or a yield sign, and you are looking at a regular polygon. Defined, a regular polygon is a flat shape with straight sides whose sides and angles are all equal. These types of shapes all sort of look like they want to be circles. It almost looks like each corner of the shape is reaching out as far as it can to touch the circle. And if you drew a circle around each shape, you would see that each corner actually does touch the circle. Try it for yourself and see.


In this lesson, we are going to find the area of a regular polygon. To do this, one of the things we need to know is the number of sides our regular polygon has. We usually call this number n in formulas. We leave it as n because this number changes depending on what kind of regular polygon we have. The kind is determined by how many sides it has.

So, a regular polygon with 8 sides will have the n equal to 8, and we would plug in 8 wherever we see the n in formulas.

We also need to know the length of each side. Because all the sides of a regular polygon are equal, we just need to know the length of one side.

The Apothem

Another measurement that we need for the area is the apothem, the distance from the center of a regular polygon to the middle of any of its sides. If we drew a line from each corner of a regular polygon to the center, we will have broken our regular polygon into a number of small triangles. The apothem can then be likened to the height of each of these small triangles.

Finding the Area Using the Apothem

The formula to find the area of any regular polygon is this:

Area of Regular Polygon = n * (side length) * (apothem) / 2

So, this formula is telling us to multiply the apothem, the number of sides, and the length of a side together and then to divide by 2. Let's see how this works with a sample polygon.

Sample polygon for example problem
example of a polygon

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account