Teaching Students About Decagons

What is a Decagon?

A decagon is a polygon easily identified by one key trait – a ten-sided shape with ten interior angles and ten vertices. However, it’s important to remember 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.

Decagons are two-dimensional shapes. Two-dimensional shapes are flat and only have two dimensions: length and width. They include squares, rectangles, circles, triangles, and more. All 2D shapes can be measured by their length and width or length and height. But remember, 2D shapes are entirely flat.

Keep reading to learn all about this ten-sided shape!

Types of Decagon

Just like any polygon, there exist two ways in which a decagon can exist – regular or irregular. In polygonal terms, regular means a shape is equal-length sides and equal-measure interior angle, while irregular means it is not restricted to congruent angles or sides.

Comparatively, the regular decagon is far easier on the eye with a more elegant, pleasing shape. This is why regular decagons are popularly used for coins (like those from Australia, Belize, and Hong Kong). Irregular decagons must have ten sides closing in a space, but the lengths of their sides can vary greatly.

Concave and Convex Decagons

The majority of polygons can be either convex or concave. Convex decagons, for instance, protrude outwards and do not possess any interior angles greater than 180°. On the flip side, concave decagons have indentations, which create interior angles greater than 180°.

Regardless of whether a decagon is concave or convex, it possesses the following qualities:

  • It is a ten-sided shape
  • It has ten vertices
  • It has ten interior angles

All decagons share the above properties, including regular, irregular, concave, and convex. However, there is one property that is unique to concave and convex decagons:

  • Their interior angles always add up to 1,440°

Simple and Complex Decagons

Decagons can either be simple or complex. Simple decagons have no sides that cross over themselves, and they follow all of the conventional rules of polygons.

A standard regular decagon meets all these requirements:

  • Regular decagon
  • Convex decagon
  • Simple decagon

On the other hand, complex decagons are self-intersecting, meaning that their sides cross over each other. Despite having additional interior spaces because their sides cross over one another, complex decagons are still technically classified as a ten-sided shape, with ten interior angles and ten vertices. Because they are so irregular, complex decagons do not follow any rules.

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