# Octagon in Geometry: Definition, Properties & Formula

Coming up next: Tetrahedron: Definition & Formula

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

Replay
Your next lesson will play in 10 seconds
• 0:05 What is an Octagon?
• 0:41 Properties of an Octagon
• 1:57 Area of an Octagon
• 2:42 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay
Speed

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Octagons appear in real life in all sorts of places: architecture, engineering, and even nature. In this lesson, explore the properties of an octagon, learn how to find the area of a regular octagon and review what you've learned with a short quiz.

## What Is an Octagon?

An octagon is a geometrical shape that contains eight sides and eight angles. Octagons must have straight sides that connect; they cannot be curved or disconnected. You will often see octagons in real life in the shape of a stop sign.

At one time, you could also see octagons used in architecture. Houses were once made in North America in an octagonal shape because they were believed to be cheaper to build and easier to heat and cool. Few of these houses remain standing today, but we can still appreciate the usefulness of octagons in other areas of life!

## Properties of an Octagon

Octagons can either be regular or irregular. Any shape with eight straight, connected sides is an octagon. Where and how those sides connect, and the length of the sides, determines whether or not the octagon is regular.

Regular octagons have sides that are congruent. That means that all of the sides of the octagon are the same measurement. They also have congruent angles, which means that the measurement of all of the angles is the same, too. The exterior angles of a regular octagon are all 135 degrees and the interior angles are all 45 degrees.

As you can see from the image above, exterior angles are the angles along the edge of the octagon, while interior angles are created by drawing two diagonals inside the octagon.

Irregular octagons have sides that are not congruent, which means that they aren't all the same measurement. They can also have points that are facing inward and outward. An octagon that has points that are facing inward is a concave octagon.

It is important to note that regular octagons are always classified as convex octagons, while irregular octagons can be either concave or convex.

## Area of an Octagon

The area of a regular octagon can be found by using this formula:

To unlock this lesson you must be a Study.com Member.

### Register to view this lesson

Are you a student or a teacher?

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### 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.