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Octagon – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">OctagonOctagon – Definition, ExamplesTable of ContentsOctagons: Definition, Properties, and Examples Definition of Octagons

An octagon is a polygon with eight sides and eight angles. It belongs to the polygon family, which includes shapes with at least three straight sides and angles. Octagons have special properties: they have 20 diagonals, interior angles that sum up to 1,080°, and exterior angles that sum up to 360°. In a regular octagon, each interior angle measures 135°.

Octagons can be classified into different types based on their sides and angles. A regular octagon has eight equal sides and eight equal angles, while an irregular octagon has unequal sides and angles. Based on how the angles point, octagons can also be convex (all angles pointing outwards) or concave (at least one angle pointing inwards). A convex octagon has no interior angle greater than 180°, while a concave octagon has at least one interior angle greater than 180°.

Examples of Octagons Example 1: Finding the Perimeter of a Regular Octagon Problem:

If the length of the side of a regular octagon is 10 cm, find its perimeter.

Regular octagon

Step-by-step solution:

Step 1, Look at what we know. The side length of our regular octagon is 10 cm.

Step 2, Think about how to find the perimeter. The perimeter means the total distance around the shape.

Step 3, Use the formula for perimeter of a regular octagon. Since all sides have the same length, we can multiply: perimeter = 8 × side length.

Step 4, Calculate the perimeter by plugging in our side length. Perimeter = 8 × 10 = 80 cm.

Example 2: Finding the Side Length of a Regular Octagon Problem:

If the perimeter of a regular octagon is 200 cm, find the length of its side.

Regular octagon

Step-by-step solution:

Step 1, List what we know. The perimeter of the regular octagon is 200 cm.

Step 2, Remember the formula for perimeter of a regular octagon: perimeter = 8 × side length.

Step 3, Set up an equation to find the side length. 8 × side length = 200 cm.

Step 4, Solve for the side length by dividing both sides of the equation by 8. Side length = 2008\frac{200}{8}8200​ = 25 cm.

Example 3: Finding the Perimeter of an Irregular Octagon Problem:

Find the perimeter of an irregular octagon whose side lengths are 6 cm, 16 cm, 14 cm, 20 cm, 12 cm, 8 cm, 10 cm, and 18 cm.

Irregular octagon

Step-by-step solution:

Step 1, Understand what an irregular octagon is. It's an octagon where the sides are not all the same length.

Step 2, Learn how to find the perimeter of an irregular shape. We need to add up all the side lengths.

Step 3, Add all eight side lengths together. Perimeter = (6 + 16 + 14 + 20 + 12 + 8 + 10 + 18) cm.

Step 4, Calculate the sum of all sides. Perimeter = 104 cm.

Comments(11)BBadmintonPlayerScarlettNovember 5, 2025This octagon def is great! Helped my students grasp the concept easily. Clear examples made perimeter calcs a breeze.

MCMs. CarterSeptember 17, 2025I’ve been helping my kids with geometry, and this octagon page was a lifesaver! The clear examples made perimeter calculations so much easier to explain. Great resource for parents and teachers!

NNatureLover82September 17, 2025I used this page to help my kids understand octagons for their geometry homework—it explained everything so clearly! The examples on perimeter really helped make it click for them. Thanks, EDU!

NNatureLover85September 10, 2025I used this octagon definition and examples to help my kids with their geometry homework. The clear explanation of diagonals and angles made it so easy for them to understand. Thanks for such a helpful resource!

MCMs. CarterSeptember 10, 2025I used the octagon definition and examples from this page to help my kids with their geometry homework. It’s super clear, and the perimeter problems were a great practice. Thanks for making math easier to teach!

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