All About Octagons: What Does An Octagon Look Like? + Examples

20 May, 2025

Ever stopped at a stop sign and wondered about the shape staring back at you? That shape, my friends, is an octagon, and it's far more fascinating than you might think.

At its most basic, an octagon is a polygon – a closed, two-dimensional shape – with eight sides and eight angles. The word itself comes from the Greek "octa," meaning eight, and "gon," meaning angle. But the world of octagons extends beyond simple definitions. While the iconic stop sign provides a readily recognizable image, not all octagons are created equal. The beauty of geometry lies in its variations, and the octagon is no exception.

Aspect	Details
Definition	A polygon with eight sides and eight angles.
Types	Regular, Irregular, Convex, Concave
Regular Octagon	All sides and angles are equal.
Irregular Octagon	Sides and/or angles are not all equal.
Convex Octagon	All interior angles are less than 180 degrees.
Concave Octagon	At least one interior angle is greater than 180 degrees.
Perimeter (Regular)	8 side length
Perimeter (Irregular)	Sum of all side lengths
Interior Angle Sum	1080 degrees
Each Angle (Regular)	135 degrees
Examples	Stop signs, some architectural designs, UFC fighting arena
Further Resources	Math is Fun - Octagon

Consider the regular octagon. This is the pristine, symmetrical version where all eight sides are of equal length, and all eight interior angles are equal, each measuring 135 degrees. Its perfect symmetry lends itself to certain applications, like the aforementioned stop sign. The uniform shape is easily recognizable and conveys a sense of order and stability. A regular octagon boasts eight lines of symmetry, each capable of dividing the shape into two perfectly mirrored halves. It also possesses rotational symmetry of order 8, meaning it can be rotated by multiples of 45 degrees and still appear identical to its original form.

However, step away from this ideal and you enter the realm of the irregular octagon. This is where things get interesting. An irregular octagon is any eight-sided polygon where the sides are not all the same length and/or the angles are not all the same measurement. This doesn't mean it ceases to be an octagon; it simply means it lacks the perfect uniformity of its regular counterpart. Think of it as the rebel cousin of the geometry family. It still adheres to the fundamental rule of having eight sides, but it breaks free from the constraints of perfect symmetry.

The perimeter of a regular octagon is straightforward to calculate: simply multiply the length of one side by eight. But when dealing with an irregular octagon, the perimeter becomes a bit more involved. You must measure the length of each of the eight sides individually and then add them together. This highlights a crucial difference: while regular shapes offer neat, concise formulas, irregular shapes often require more direct measurement and calculation.

Another important distinction lies in the angles. While the interior angles of a regular octagon each measure 135 degrees, the angles of an irregular octagon can vary. However, there's a fundamental rule that applies to all octagons, regardless of their regularity: the sum of their interior angles must always equal 1080 degrees. This is a consequence of the fact that an octagon can be divided into six triangles, and the sum of the angles in each triangle is 180 degrees (6 180 = 1080). So, even though an irregular octagon may have angles of varying sizes, their total will always reach this consistent value.

Beyond regularity, octagons can also be classified as convex or concave. A convex octagon is one where all its interior angles are less than 180 degrees. Imagine placing a ruler along any side of the octagon; the entire shape will lie on one side of the ruler. In contrast, a concave octagon has at least one interior angle greater than 180 degrees. This means that at least one vertex "points inward," creating a dent in the shape. If you were to place a ruler along a side adjacent to this inward-pointing vertex, part of the octagon would lie on one side of the ruler, and another part would lie on the other side.

The stop sign serves as an excellent example of a regular, convex octagon. Its uniform sides and angles, combined with its outward-pointing vertices, make it a textbook case of this geometric form. However, imagine an octagon where one of the vertices is pushed inward, creating a dent. This would transform the shape into a concave octagon, even though it would still retain its eight sides and eight angles.

The ubiquity of the stop sign has ingrained the image of a regular octagon in our minds. Its red color and white lettering further enhance its recognizability, making it a universal symbol for halting traffic. Drivers are trained to associate this shape with the imperative to come to a complete stop, check for cross-traffic, and proceed only when it is safe to do so. The stop sign's placement at intersections and crosswalks reinforces its role in ensuring pedestrian and vehicular safety.

However, the applications of the octagon extend far beyond traffic control. Architects have long been drawn to its unique properties, incorporating it into building designs and floor plans. The Castel del Monte in Apulia, Italy, is a prime example of octagonal architecture. This 13th-century castle features an octagonal plan with eight towers, showcasing the geometric elegance of the octagon. Its symmetrical design and sturdy construction have allowed it to withstand the test of time, serving as a testament to the enduring appeal of this shape.

The Ultimate Fighting Championship (UFC) uses an octagon-shaped enclosure, often referred to as "The Octagon," for its mixed martial arts events. This eight-sided cage provides a contained space for fighters to compete, preventing them from falling out of the ring. The shape also allows for strategic maneuvering and enhances the viewing experience for spectators. The UFC's use of the octagon has further popularized the shape, associating it with the intensity and excitement of combat sports.

In geometry, the octagon provides a fascinating case study in the interplay between regularity and irregularity, convexity and concavity. Understanding these distinctions is crucial for accurately describing and analyzing geometric shapes. While regular octagons offer simplicity and symmetry, irregular octagons challenge our assumptions and highlight the diversity within geometric forms. Whether it's a stop sign, a medieval castle, or a fighting arena, the octagon continues to shape our world in unexpected and profound ways.

When calculating the area of an octagon, the approach depends on whether it's regular or irregular. For a regular octagon, there are specific formulas that utilize the side length or other properties to determine the area. However, for an irregular octagon, calculating the area can be more complex, often requiring dividing the shape into smaller, more manageable components, such as triangles and rectangles, and then summing their individual areas.

The term "rectangular octagon" is somewhat of a misnomer. An octagon, by definition, has eight sides. A rectangle, on the other hand, has four sides. It's possible to create an octagon that incorporates rectangular elements within its design, but it wouldn't be a true "rectangular octagon." The fundamental requirement of eight sides must always be met for a shape to be classified as an octagon.

So, the next time you encounter an octagon, whether it's a stop sign on the street or a decorative element in a building, take a moment to appreciate its geometric complexity. It's a shape that embodies both order and variation, symmetry and asymmetry, convexity and concavity. It's a reminder that even within the seemingly rigid rules of geometry, there's always room for creativity and surprise.

Consider the challenge of drawing an octagon. A regular octagon can be constructed using a compass and straightedge, following a specific set of geometric instructions. This process involves creating a circle, dividing it into eight equal parts, and then connecting the points to form the octagon's sides. However, drawing an irregular octagon is more freeform, allowing for greater artistic license in determining the side lengths and angles.

In conclusion, the octagon is more than just a shape; it's a testament to the power and versatility of geometry. From its practical applications in traffic control to its aesthetic appeal in architecture and design, the octagon continues to captivate and inspire. Its eight sides and eight angles create a framework for endless possibilities, reminding us that even the most basic geometric forms can hold profound beauty and complexity.

An octagon is an 8 sided figure and looks like a stop sign.

An octagon is a closed shape with eight sides and the lengths aren’t always equal so it doesn’t always look like a stop sign this is called an irregular octagon.

What is an example of an octagon?

How does an octagon look like?

This is a octagona octagon has 8 sides and 8 corners.1 face and 8 lines of symmetry. *an octagon need not have any lines of symmetry.

What does an octagon look like?

Perimeter of a regular octagon.

The formula to calculate the perimeter of a regular octagon shape = 8 side.

Here, “side” refers to the length of the equal sides of a regular octagon.

Perimeter of an irregular octagon.

For an irregular octagon shape, the perimeter is calculated by adding together the individual side lengths.

It is a shape that has 8 sides but does not look like a regular octagon.

As long as it has 8 sides it is an irregular octagon.

The stop sign shape is an octagon, characterized by its eight sides and red color with white lettering.

This design universally signifies that drivers must come to a complete stop and only proceed when the path is clear and safe.

Drivers must stop at the stop line, crosswalk, or intersection, whichever they encounter first.

What does irregular octagon look like?

It is a shape that has 8 sides but does not look like a regular octagon.

As long as it has 8 sides it is an irregular octagon.

A regular octagon must have sides of equal length.

This octagon has two sides that are longer than the other 6 sides.

That makes it an irregular octagon.

The answer is convex octagon.

How did we get here?

A concave octagon has some vertices that point inward.

A convex octagon has no vertices that point inward.

What does an octagon shape look like?

An octagon is an eight sided polygon.

How many sides does a circle have?

Not all of an irregular octagon’s sides are equal in length, and their angles aren’t equal either.

But the sum of these angles is still equal to 1080°, just like a regular octagon.

Put simply, an irregular octagon has unequal sides and unequal angles, but the sum of these angles equals the same value as a regular octagon.

For an octagon to be classed as an octagon, it has to have a certain amount of angles that add up to a larger number.

If it's a regular octagon, these angles will add up to 1080.

When that's divided by 8 (the amount of sides) that's 135 degrees per angle.

An octagon is a polygon that has eight sides.

What does an octagon look like?

An octagon is an 8 sided figure and looks like a stop sign.

An octagon is a closed shape with eight sides and the lengths aren’t always equal so it doesn’t always look like a stop sign this is called an irregular octagon.

What are the dimensions of an octagon?

The whole ufc octagon (the part surrounded by the fence and the part outside the

What does an octagon look like?

A octagon looks like a stop sign.

What does a rectangular octagon look like?

In this octagon area calculator, you will also find the answers to the following questions:

What is an octagon, how many sides does an octagon have, how to find the area of a regular octagon or how to draw an octagon.

We will review the octagon definition, discuss the octagon angles and how they affect the octagon shape.

What angles are an octagon?

An octagon contains six triangles, or 1080 degrees.

This means with 8 angles, each angle is 135 degrees.

What does an octagon shape look like?

A regular octagon is a closed shape with sides of equal length and interior angles of the same measurement.

It has eight symmetric lines and rotational equilibrium of order 8.

Look at the image below and determine if it’s an octagon or not.

Look for the characteristics of an octagon.

An octagon is an 8 sided shape with 8 vertices and 8 angles.

This shape has 7 sides, vertices and angles.

2 state whether or not the shape is an octagon.

This shape is not an octagon.

An octagon is a shape that is made up of eight straight sides and eight angles.

(think of a stop sign!) it has no curves and is a closed shape (no openings).

If you still can’t quite picture what does an octagon look like, just scroll down a little bit and check out the printable!

How many sides does an octagon have?

Now that we have an side length of m, we can find the area of the entire regular octagon.

Have students generate the area expression below by summing the smaller areas within the octagon.

Then, substitute the value we found for m.

What does our area expression look like now?

Ask students to simplify the equation.

Learn how to calculate its area, circumradius, inradius, span and other properties using various formulas and examples.

An octagon is a polygon with eight sides and angles.

Learn how to find its perimeter, area, diagonals, angles and types with formulas and examples.

Learn what an octagon is, how to identify its types and properties, and how to calculate its perimeter.

See examples of octagons in real life and compare them with other polygons.

Learn what an octagon is, how it is formed, and how it differs from other polygons.

Explore the historical and cultural significance of the octagon in architecture, design, and symbols.

Learn how to identify regular, irregular, convex and concave octagons, and their area and width formulas.

An octagon is a polygon with eight sides and angles.

Learn about the different types of octagons, their properties, formulas and examples of octagons in geometry and everyday objects.

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