Decagon: Definition & Shape

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  • 0:02 What Are Polygons?
  • 0:30 Regular & Irregular
  • 1:53 Concave & Convex
  • 2:27 Simple & Complex
  • 3:28 Real World Decagons
  • 3:54 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, we'll discuss the different types of decagons, such as regular and irregular, convex and concave, and simple and complex. Then, you can test your knowledge with a brief quiz.

What Are Polygons?

In general, we call a lot of things shapes. We have circles, triangles, squares, rectangles. . . we could go on and on. But only certain shapes are polygons.

Polygons are closed, 2-dimensional shapes with straight sides. This definition leaves out circles and ovals, but still leaves room for lots of shapes to be polygons. In this lesson, we'll focus on the decagon.

Regular and Irregular Decagons

A decagon is a 10-sided polygon. It also has ten vertices - which is where the sides meet - and ten angles. The regular decagon is probably the most recognizable one. It's called a regular decagon because all its sides and angles are congruent, or equal in size.

In this next illustration, the vertices are circled.

Regular decagon with the vertices circled.
regular decagon with vertices circled

In a regular decagon, all the angles measure 144 degrees. So, the sum of a regular decagon's angles is always 1,440 degrees.

Not all decagons are regular, however. As previously stated, a decagon is simply a 10-sided polygon, so decagons can take on various forms as long as they're closed and have ten sides. This is an irregular decagon because the sides and angles are not congruent:

Irregular decagon.
decagon with unequal sides

Even though this decagon is irregular, it still has ten sides, vertices and angles. Here's the same decagon with the ten vertices and angles circled:

Irregular decagon with the vertices circled.
irregular decagon with vertices circled

Here's another irregular decagon:

This star is an irregular decagon.
five pointed star

Don't forget, though, that a polygon is a closed shape; so even if a figure has ten sides, if it's not closed, it's not a decagon:

This is not a decagon because it is not a closed shape.
non closed ten sided figure

The figure you're looking at does, indeed, have ten sides, but it's not closed, so it doesn't have ten vertices or angles and is not a decagon.

Concave and Convex Decagons

This irregular decagon that we've already examined is also concave because it contains angles larger than 180 degrees.

All the blue angles are larger than 180 degrees.
irregular decagon with concave sections indicated

This decagon is also concave, with angles larger than 180 degrees.

All the blue angles are larger than 180 degrees.
five pointed star with concave sections indicated

The regular decagon, however, is convex, or the opposite of concave, because all of its angles are smaller than 180 degrees.

All the angles are smaller than 180 degrees, so this decagon is convex.
regular decagon

An easy way to remember the difference between convex and concave is to think of a concave decagon as being 'caved in' at one of the corners.

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