Mathematics students from countries as far-flung together Australia, Belize and also Hong Kong may have actually everyday call with decagons, since those countries have offered the 10-sided shape in their coins. Many of us, though, just encounter decagons in math class and also when feeling particularly patriotic.

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Decagons room Polygons

Decagons belong come the family of two-dimensional shapes called polygons. Polygons get their surname from Greek, an interpretation "many-angled," because all polygons have multiple interior angles. Castle close in a two-dimensional space using just straight sides.


How many Sides does A Decagon Have?

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

Properties that Decagons

For a polygon to be a decagon, the must have these identify properties:

10 sides10 interior angles10 vertices

Decagon Angles

In plenty of decagons, the sum of interior angles will be 1,440°, however that is not an identifying home because facility decagons will not have actually that sum.

Regular decagons have two extr identifying properties:

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


Drawing a decagon bring away no skill; simply attract 10 heat segments the connect, and you have it. Illustration a regular, convex decagon, however, takes real skill, because each internal angle have to be 144°, and all sides must be equal in length.

Drawing a concave decagon is actually fairly easy: do a five-pointed star and fill the in. The is the star that appears 50 times on our country"s flag, and the synopsis of such a pentagram (five-pointed star) is a decagon. That method you see a the majority of decagons anytime girlfriend are close to our flag:


Be mindful to recognize the difference between the five-pointed pentagram (the lines cross themselves) and the decagon (either simply the overview of a pentagram or a solidly to fill pentagram).

Decagon Definitions


A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices i beg your pardon is whereby the political parties meet.A regular decagon has 10 equal-length sides and equal-measure internal angles. Each angle actions 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, v no internal angle higher than 180°.A concave decagon have indentations, producing interior angles higher than 180°.A simple decagon does no have any type of sides the cross or intersect.A complex decagon has self-intersecting sides, is complex, and also highly irregular.

Regular and Irregular Decagons

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


Because it is a an overwhelming shape to make, the regular, convex decagon is popular with coins (like those from Australia, Belize and Hong Kong). Rarely often rare decagons need to simply have actually 10 sides closing in a space, yet the lengths of your sides deserve to vary greatly.

Concave and also Convex Decagons

Most polygons have the right to be convex or concave. Convex decagons bulge outward, with no inner angle greater than 180°. Concave decagons have actually indentations, developing interior angles higher than 180°. That is why the synopsis of a five-pointed star is a concave decagon; that has five interior angles each of i beg your pardon is far greater 보다 180°.


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

10 sides10 vertices10 internal angles

Simple and complicated Decagons

Decagons can be straightforward or complex. A basic decagon has actually no political parties crossing themselves. A an easy decagon adheres to all the standard "rules" that polygons.


By contrast, a complicated decagon is self-intersecting. In crossing its very own sides, a complicated decagon to adjust off extr 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 require not follow any predictable rule around interior angle or your sums.

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

Regular decagonConvex decagonSimple decagon

So, to be absolutely specific (and maybe a bit fussy) girlfriend can define this figure as a regular, convex, straightforward decagon:

Decagon Shapes

Below are numerous decagons. See, without looking in ~ the identifying information, if you can determine whether each is constant or irregular, convex or concave, straightforward or complex. Mental to name all the attributes, in situation a shape fits an ext than one category.

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In order, those decagons are:

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

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

Lesson Summary

Now the you have actually studied this lesson, you space able to recognize and also define a decagon, state the identifying nature of all decagons, and the identifying nature of regular decagons. You are also able to identify as decagons the stars on the U.S. Flag, and identify the differences between regular and also irregular decagons; basic and complex decagons; and concave and also convex decagons.