What is an octagon?
An octagon is a 2D shape with eight sides, eight angles, and eight vertices.
Octagons can be regular or irregular. This depends on their shape and how they’ve been drawn.
Regular and Irregular Octagons
Regular octagons
When all sides and angles are equal, an octagon is regular.
Regular octagons also have the following:
- interior angles of 135°
- exterior angles of 45°
When you add up all the corners of an octagon, it equals 1080°. So when it comes to figuring out the total area of an octagon, we need to use the formula:
In this equation, a stands for the length of one of its sides.
Irregular octagons
Irregular octagons do not all have equal sides and angles.
The above example is also a concave octagon with an inward angle. Octagons without inward angles are called convex octagons.
What’s shaped like octagons in real life?
There are lots of things in daily life that are shaped like octagons. All you’ve got to do is look for them! The next time you’re out and about, why don’t you see how many things you can spot that are octagons? They don’t just have to be regular octagons, either. As long as they’ve got eight sides, they’re octagon shaped. Here’s a list of things we’ve found; see if you can think of yourself!
- Umbrellas – Deeding on the size of your umbrella, it’s usually octagon shaped. This allows lots of support while keeping the support beams out of your way. If umbrellas were square, the supports would need to be further down the handle to be as strong.
- Signs – In the UK, most stop signs are octagon shaped. There are hardly any other signs that take this shape. This makes stop signs more identifiable for drivers. Having to stop is essential when driving, so these signs need to be recognizable.
- Tiles – Now, we’re not saying every tile in the world is octagon shaped, but some are. This is because octagons slot together well. They’re also an excellent shape and can stand out.
Octagon Angles
For an octagon to be classed as an octagon, it has to have a certain amount of angles that add up to a more significant number. If it’s a regular octagon, these angles will add up to 1080. When that’s divided by 8 (the number of sides), that’s 135 degrees per angle.
If you want to make an irregular octagon, ensure all the angles add up to 1080 degrees. However, all the sides of the shape can be different lengths. Octagon angles can vary depending on whether you want a regular or irregular octagon.
