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Decagon
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Geometry Hub / Polygons / Decagon
05.17 • Polygons

Decagon

Study decagon through its ten-sided boundary and the regular case's clean one-hundred-forty-four-degree interior angles.

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

Decagon Diagram

Track the ten edges, then compare the side-count name with the regular decagon's angle and diagonal structure.

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

Definition: A decagon is a polygon with ten sides.
Detailed definition

Understanding Decagon

Decagon is a polygon with ten sides. A decagon is a polygon with ten sides. Like all named polygons, the word decagon tells you the side count before it tells you anything about regularity or symmetry.

A regular decagon has equal sides and equal interior angles of one hundred forty-four degrees. Its exterior angles are thirty-six degrees, which connects it nicely to pentagon-based angle patterns in the regular case.

This polygon is useful because the ten-side count leads to rich but still manageable combinatorial facts such as many diagonals and a large interior angle sum, while staying close to familiar decimal counting.

Key facts

Important ideas to remember

  • A decagon is a polygon with ten sides.
  • A decagon has ten sides, ten vertices, and an interior angle sum of one thousand four hundred forty degrees.
  • Each interior angle of a regular decagon measures one hundred forty-four degrees.
  • A decagon has thirty-five diagonals in total.
Where it is used

Where decagon shows up

  • Use decagon naming in polygon classification and side-count exercises.
  • Use regular-decagon angles in symmetry and angle-measure problems.
  • Use the shape to compare polygon diagonals and interior sums across different side counts.
Common mistakes

What to watch out for

  • Do not mix the regular decagon's angle values into irregular decagon cases automatically.
  • Do not lose count in a shape with many short sides and many diagonals.
  • Do not confuse ten sides with ten diagonals; those are different counts entirely.
Worked examples

Decagon 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 decagon 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 decagon 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 decagon is a useful benchmark for ten-sided polygon thinking. It links the naming rule to regular-angle values and a larger diagonal count without becoming visually overwhelming.

Do

What you can do here

  • Count the ten sides and compare the result with the regular decagon angle values.
  • Explore how diagonals and angle totals grow as side count increases.
  • Save a clean decagon diagram for naming, angle, or diagonal review.
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

Decagon

Handle larger named polygons with more confidence.

2

Decagon

Connect side count to diagonal and angle growth more clearly.

3

Decagon

Use regular-decagon information without losing the broader polygon picture.

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.

05.16

Previous: Nonagon

A nonagon is a polygon with nine sides.

05.18

Next: Dodecagon

A dodecagon is a polygon with twelve sides.