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

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Decagons are Polygons

Decagons belong to the family members of two-dimensional shapes dubbed polygons. Polygons get their name from Greek, meaning "many-angled," because all polygons have actually multiple inner angles. They close in a two-dimensional room using only straight sides.


How countless Sides does A Decagon Have?

A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is whereby the sides meet.

Properties of Decagons

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

10 sides10 interior angles10 vertices

Decagon Angles

In countless decagons, the amount of interior angles will be 1,440°, however that is not an identifying building because complicated decagons will certainly not have that sum.

Regular decagons have two extr identifying properties:

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


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

Drawing a concave decagon is actually relatively easy: do a five-pointed star and also fill that in. The is the star that shows up 50 times on ours country"s flag, and also the rundown of together a pentagram (five-pointed star) is a decagon. That way you view a the majority of decagons anytime you are close to our flag:


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

Decagon Definitions


A decagon is a 10-sided polygon, through 10 internal angles, and also 10 vertices i beg your pardon is where the sides meet.A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle actions 144° and they all add up come 1,440°.An irregular decagon has sides and also angles that are not all equal or congruent.A convex decagon bulges outward, with no internal angle greater than 180°.A concave decagon have indentations, producing interior angles higher than 180°.A simple decagon does not have any sides that cross or intersect.A complex decagon has actually self-intersecting sides, is complex, and also highly irregular.

Regular and also Irregular Decagons

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


Because that is a daunting shape come make, the regular, convex decagon is renowned with coins (like those from Australia, Belize and also Hong Kong). Irregular decagons must simply have 10 political parties closing in a space, but the lengths of your sides deserve to vary greatly.

Concave and Convex Decagons

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


So far all the decagons debated -- regular, irregular, concave, and convex -- re-publishing the very same properties:

10 sides10 vertices10 inner angles

Simple and facility Decagons

Decagons have the right to be simple or complex. A basic decagon has actually no political parties crossing themselves. A simple decagon complies with all the conventional "rules" that polygons.


By contrast, a complex decagon is self-intersecting. In crossing its very own sides, a complex decagon set off additional interior spaces, however it is still stated to have actually only 10 sides, 10 inner angles, and 10 vertices. Due to the fact that it is so very irregular and self-intersecting, a complex decagon require not follow any predictable rule around interior angles or your sums.

Notice that a solitary decagon can fit right into several categories. The standard regular decagon meets all these requirements:

Regular decagonConvex decagonSimple decagon

So, to be absolutely precise (and possibly a little fussy) you can explain this figure as a regular, convex, straightforward decagon:

Decagon Shapes

Below are several decagons. See, there is no looking in ~ the identify information, if you deserve to determine whether each is continuous or irregular, convex or concave, basic or complex. Psychic to name 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, basic decagona complicated decagona concave, basic decagon

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

Lesson Summary

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