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Octagon
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Geometry Hub / Polygons / Octagon
05.15 • Polygons

Octagon

Study octagon as an eight-sided polygon and use the regular case to connect side count with one hundred thirty-five degree interior angles.

Interactive diagram Live labels and measurements Worked examples PNG graph downloads
Octagon
Interactive diagram

Octagon Diagram

Track the eight sides and compare how the shape behaves in regular and irregular forms.

Use the movable diagram to see what defines octagon, how the labels relate to the figure, and what stays true as the board changes.

Definition: An octagon is a polygon with eight sides.
Detailed definition

Understanding Octagon

Octagon is a polygon with eight sides. An octagon is a polygon with eight sides. The side count remains the defining feature whether the polygon is regular or irregular.

A regular octagon has especially memorable angle behavior: each interior angle is one hundred thirty-five degrees, and each exterior angle is forty-five degrees. Because the side count is even, opposite sides in the regular case are parallel.

Octagons are useful because they show how named polygons can carry both a simple counting rule and a richer set of regular-case properties when symmetry is added.

Key facts

Important ideas to remember

  • An octagon is a polygon with eight sides.
  • An octagon has eight sides, eight vertices, and an interior angle sum of one thousand eighty degrees.
  • Each interior angle of a regular octagon measures one hundred thirty-five degrees.
  • In a regular octagon, opposite sides are parallel.
Where it is used

Where octagon shows up

  • Use octagon naming in side-count and polygon-classification work.
  • Use regular-octagon facts in angle, symmetry, and design-related geometry problems.
  • Use octagons to compare even-sided polygon behavior with odd-sided polygon behavior.
Common mistakes

What to watch out for

  • Do not confuse the regular octagon's angle values with the angles of every octagon.
  • Do not lose the side count in a highly symmetric or nearly circular-looking regular case.
  • Do not mix octagon with decagon just because both have many sides.
Worked examples

Octagon examples

Use these worked examples to see the idea in a clean diagram first, then in the kind of reasoning students usually need for classwork, homework, or test practice.

Example 1

Example 1: Naming a octagon from its side count

Count the sides and vertices carefully so the polygon name comes from the correct total.

  • Start at one vertex and count around the boundary once.
  • Match the count to the standard polygon name.
  • Check that the shape closes after the final side.

Result: The polygon is named accurately because the side count and vocabulary agree.

Example 2

Example 2: Connecting octagon to its regular form

Use the same side count to discuss the regular version of the polygon without changing the name itself.

  • Keep the side count fixed.
  • Notice how equal sides and equal angles change the look of the figure.
  • Separate the naming rule from the regularity rule.

Result: The student can name the polygon first and then discuss whether it is regular or irregular.

For

Why this page helps

This page helps because octagon is a widely recognized named polygon, yet students often remember the name without linking it to its regular-angle structure or even-side symmetry.

Do

What you can do here

  • Compare the eight-sided boundary with the one-hundred-thirty-five-degree regular angle pattern.
  • Watch regular and irregular octagons share the same name while changing in symmetry.
  • Download a clear octagon diagram for naming, angle, or symmetry study.
Learning outcome

What this page helps you do

These takeaways are meant to help you recognize the idea faster, read diagrams more accurately, and use the topic with more confidence in real problems.

1

Octagon

Recognise octagons from both count and regular-angle structure.

2

Octagon

Use even-sided regular polygon ideas more confidently.

3

Octagon

Link side-count vocabulary to stronger measurement insight.

05

Back to Polygons

Return to the category page to open another concept in polygons.

ST

Geometry Construction Studio

Use a dedicated geometry drawing board for points, segments, rays, lines, angles, circles, triangles, rectangles, pencil sketches, and virtual measuring tools.

05.14

Previous: Heptagon

A heptagon is a polygon with seven sides.

05.16

Next: Nonagon

A nonagon is a polygon with nine sides.