Mathematics students from nations as far-flung as Australia, Belize and also Hong Kong may have everyday call with decagons, due to the fact that those countries have used the 10-sided shape in your coins. Many of us, though, only encounter decagons in mathematics class and also when feeling specifically patriotic.

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Decagons space Polygons

Decagons belong come the family of two-dimensional shapes dubbed polygons. Polygons acquire their name from Greek, meaning "many-angled," since all polygons have multiple interior angles. Lock close in a two-dimensional space using only straight sides.


How many Sides go A Decagon Have?

A decagon is a 10-sided polygon, v 10 internal angles, and also 10 vertices i m sorry is wherein the sides meet.

Properties that Decagons

For a polygon to it is in a decagon, the must have these identify properties:

10 sides10 inner angles10 vertices

Decagon Angles

In plenty of decagons, the sum of inner angles will be 1,440°, but that is not an identifying residential or commercial property because complicated decagons will certainly not have that sum.

Regular decagons have two additional identifying properties:

10 exterior angle of 36°, summing come 360°10 internal angles the 144°, summing to 1,440°


Drawing a decagon takes no skill; simply attract 10 line segments that connect, and you have actually it. Illustration a regular, convex decagon, however, takes real skill, because each inner angle must be 144°, and also all sides must be equal in length.

Drawing a concave decagon is actually reasonably easy: do a five-pointed star and fill it in. That is the star that shows up 50 times on our country"s flag, and also the summary of together a pentagram (five-pointed star) is a decagon. That method you see a the majority of decagons anytime girlfriend are near our flag:


Be mindful to recognize the difference between the five-pointed pentagram (the lines cross themselves) and also the decagon (either just the synopsis of a pentagram or a solidly filled pentagram).

Decagon Definitions


A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices i m sorry is whereby the political parties meet.A regular decagon has actually 10 equal-length sides and also equal-measure inner angles. Each angle procedures 144° and also they all add up to 1,440°.An irregular decagon has actually sides and angles that are not all equal or congruent.A convex decagon bulges outward, with no interior angle greater than 180°.A concave decagon have actually indentations, creating interior angles greater than 180°.A simple decagon does no have any kind of sides that cross or intersect.A complex decagon has self-intersecting sides, is complex, and also highly irregular.

Regular and also Irregular Decagons

All polygons can be attracted as regular (equal-length sides, equal-measure inner angles) or rarely often, rarely (not minimal to congruent angle or sides). The regular, convex decagon is a subtle and also elegant shape, v 10 exterior angles of 36°, 10 internal angles that 144°, and also 10 vertices (intersections of sides).


Because the is a challenging shape to make, the regular, convex decagon is well-known with coins (like those native Australia, Belize and Hong Kong). Rarely often rare decagons need to simply have actually 10 political parties closing in a space, yet the lengths of your sides have the right to vary greatly.

Concave and also Convex Decagons

Most polygons have the right to be convex or concave. Convex decagons bulge outward, v no inner angle higher than 180°. Concave decagons have indentations, creating interior angles better than 180°. The is why the overview of a five-pointed star is a concave decagon; it has 5 interior angles each of which is much greater than 180°.


So far all the decagons questioned -- regular, irregular, concave, and convex -- share the very same properties:

10 sides10 vertices10 interior angles

Simple and complex Decagons

Decagons have the right to be an easy or complex. A straightforward decagon has actually no political parties crossing themselves. A basic decagon complies with all the typical "rules" the polygons.


By contrast, a complicated decagon is self-intersecting. In cross its very own sides, a complex decagon to adjust off added interior spaces, yet it is still stated to have actually only 10 sides, 10 interior angles, and 10 vertices. Due to the fact that it is so highly irregular and self-intersecting, a complex decagon require not follow any predictable rule around interior angle or their sums.

Notice that a solitary decagon have the right to fit right into several categories. The standard regular decagon meets every these requirements:

Regular decagonConvex decagonSimple decagon

So, to it is in absolutely specific (and possibly a little fussy) girlfriend can explain this figure as a regular, convex, straightforward decagon:

Decagon Shapes

Below are numerous decagons. See, there is no looking at the identifying information, if you can determine whether each is regular or irregular, convex or concave, basic or complex. Remember to surname all the attributes, in case a form fits more than one category.

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In order, those decagons are:

a regular, convex, an easy decagona concave, simple decagona complicated decagona concave, straightforward decagon

Did you appropriately identify all of them through all your qualities? We certain hope so!

Lesson Summary

Now the you have actually studied this lesson, you are able come recognize and define a decagon, state the identifying nature of all decagons, and the identifying nature of continuous decagons. You are also able to recognize as decagons the stars top top the U.S. Flag, and identify the differences in between regular and irregular decagons; an easy and complicated decagons; and also concave and convex decagons.