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

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Decagons room Polygons

Decagons belong come the family members of two-dimensional shapes called polygons. Polygons get their surname from Greek, an interpretation "many-angled," since all polygons have actually multiple inner angles. Castle close in a two-dimensional an are using only straight sides.


How countless Sides walk A Decagon Have?

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

Properties of Decagons

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

10 sides10 interior angles10 vertices

Decagon Angles

In countless decagons, the sum of inner angles will be 1,440°, but that is no an identifying residential or commercial property because complex decagons will certainly not have that sum.

Regular decagons have actually two additional identifying properties:

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


Drawing a decagon takes no skill; simply attract 10 line segments that connect, and you have actually it. Drawing a regular, convex decagon, however, takes genuine skill, due to the fact that each internal angle have to be 144°, and also all sides need to be equal in length.

Drawing a concave decagon is actually fairly easy: do a five-pointed star and fill that in. That is the star that shows up 50 time on our country"s flag, and also the overview of such a pentagram (five-pointed star) is a decagon. That method you watch a most decagons anytime girlfriend are close to our flag:


Be cautious to know the difference between the five-pointed pentagram (the lines overcome themselves) and also the decagon (either simply the overview of a pentagram or a solidly to fill pentagram).

Decagon Definitions


A decagon is a 10-sided polygon, v 10 inner angles, and 10 vertices which is where the sides meet.A regular decagon has actually 10 equal-length sides and also equal-measure interior angles. Every angle procedures 144° and they all include up come 1,440°.An irregular decagon has sides and also angles that are not all same or congruent.A convex decagon bulges outward, v 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 sides that cross or intersect.A complex decagon has actually self-intersecting sides, is complex, and highly irregular.

Regular and Irregular Decagons

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


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

Concave and also Convex Decagons

Most polygons can be convex or concave. Convex decagons bulge outward, through no internal angle greater than 180°. Concave decagons have indentations, developing interior angles greater 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 far greater than 180°.


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

10 sides10 vertices10 inner angles

Simple and complex Decagons

Decagons can be an easy or complex. A simple decagon has no political parties crossing themselves. A straightforward decagon follows all the traditional "rules" that polygons.


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

Notice that a single decagon can fit into several categories. The classic regular decagon meets all these requirements:

Regular decagonConvex decagonSimple decagon

So, to it is in absolutely specific (and maybe a little fussy) girlfriend can define this figure as a regular, convex, simple decagon:

Decagon Shapes

Below are numerous decagons. See, there is no looking in ~ the identify information, if you have the right to determine whether every is constant or irregular, convex or concave, an easy or complex. Mental to surname all the attributes, in instance 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 effectively identify all of them by all your qualities? We certain hope so!

Lesson Summary

Now that you have studied this lesson, you are able to recognize and define a decagon, state the identifying properties of all decagons, and also the identifying nature of regular decagons. Friend are additionally able to recognize as decagons the stars top top the U.S. Flag, and also identify the differences in between regular and also irregular decagons; straightforward and complicated decagons; and concave and also convex decagons.