Mathematics students from countries as far-flung as Australia, Belize and Hong Kong may have everyday contact with decagons, since those nations have offered the 10-sided shape in your coins. Most of us, though, only encounter decagons in math class and also when feeling specifically patriotic.

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Decagons room Polygons

Decagons belong come the family of two-dimensional shapes dubbed polygons. Polygons get their surname from Greek, definition "many-angled," since all polygons have multiple internal angles. Castle close in a two-dimensional space using only straight sides.


How numerous Sides does A Decagon Have?

A decagon is a 10-sided polygon, v 10 interior angles, and 10 vertices i m sorry is where the political parties meet.

Properties that Decagons

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

10 sides10 internal angles10 vertices

Decagon Angles

In numerous decagons, the sum of internal angles will be 1,440°, yet that is no an identifying building because facility decagons will not have actually that sum.

Regular decagons have actually two additional identifying properties:

10 exterior angles of 36°, summing to 360°10 inner angles of 144°, summing to 1,440°


Drawing a decagon take away no skill; simply attract 10 line segments the connect, and you have actually it. Illustration a regular, convex decagon, however, takes real skill, because each interior angle must be 144°, and also all sides need to be same in length.

Drawing a concave decagon is actually fairly easy: make a five-pointed star and also fill the in. The is the star that appears 50 times on our country"s flag, and also the summary of together a pentagram (five-pointed star) is a decagon. That means you see a many decagons anytime you are near our flag:


Be mindful to understand the difference in between the five-pointed pentagram (the lines overcome themselves) and also the decagon (either just the summary of a pentagram or a solidly fill pentagram).

Decagon Definitions


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

Regular and Irregular Decagons

All polygons can be drawn 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 elegant shape, with 10 exterior angle of 36°, 10 inner angles of 144°, and 10 vertices (intersections of sides).


Because the is a challenging shape to make, the regular, convex decagon is popular with coins (like those native Australia, Belize and also Hong Kong). Rarely often, rarely decagons need to simply have actually 10 sides closing in a space, yet the lengths of their sides have the right to vary greatly.

Concave and also Convex Decagons

Most polygons deserve to be convex or concave. Convex decagons bulge outward, v no inner angle higher than 180°. Concave decagons have actually indentations, creating interior angles greater than 180°. The is why the overview of a five-pointed star is a concave decagon; that has five interior angles each of i m sorry is far greater 보다 180°.


So much all the decagons disputed -- regular, irregular, concave, and also convex -- re-superstructure the very same properties:

10 sides10 vertices10 inner angles

Simple and facility Decagons

Decagons can be an easy or complex. A simple decagon has no political parties crossing themselves. A an easy decagon complies with all the conventional "rules" of polygons.


By contrast, a complicated decagon is self-intersecting. In cross its very own sides, a facility decagon set off added interior spaces, but it is still stated to have only 10 sides, 10 interior angles, and 10 vertices. Because it is so highly irregular and also self-intersecting, a complicated decagon need not follow any type of predictable rule around interior angle or their sums.

Notice the 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 accurate (and probably a little fussy) girlfriend can explain this figure as a regular, convex, basic decagon:

Decagon Shapes

Below are numerous decagons. See, without looking at the identify information, if you can determine whether every is continuous or irregular, convex or concave, simple or complex. Mental to surname all the attributes, in instance a form fits an ext than one category.

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In order, those decagons are:

a regular, convex, simple decagona concave, an easy decagona facility decagona concave, basic decagon

Did you properly identify every one of them by all your qualities? We certain hope so!

Lesson Summary

Now the you have studied this lesson, you space able to recognize and also define a decagon, state the identifying properties of every decagons, and the identifying properties of consistent decagons. Girlfriend are additionally able to identify as decagons the stars top top the U.S. Flag, and identify the differences between regular and irregular decagons; simple and complex decagons; and also concave and convex decagons.