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

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Decagons room Polygons

Decagons belong come the family of two-dimensional shapes referred to as polygons. Polygons gain their name from Greek, definition "many-angled," since all polygons have actually multiple internal angles. Lock close in a two-dimensional space using only straight sides.


How plenty of Sides walk A Decagon Have?

A decagon is a 10-sided polygon, v 10 inner angles, and also 10 vertices which is where the sides meet.

Properties the Decagons

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

10 sides10 internal angles10 vertices

Decagon Angles

In plenty of decagons, the amount of internal angles will certainly be 1,440°, but that is no an identifying property because facility decagons will not have that sum.

Regular decagons have actually two additional identifying properties:

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


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

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


Be careful to know the difference between the five-pointed pentagram (the lines overcome themselves) and the decagon (either just the synopsis of a pentagram or a solidly filled pentagram).

Decagon Definitions


A decagon is a 10-sided polygon, v 10 internal angles, and also 10 vertices which is whereby the sides meet.A regular decagon has actually 10 equal-length sides and also equal-measure internal angles. Every angle measures 144° and they all include up to 1,440°.An irregular decagon has actually sides and also angles that are not all same or congruent.A convex decagon bulges outward, through no internal angle greater than 180°.A concave decagon have indentations, developing interior angles better than 180°.A simple decagon does not have any kind of sides that 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 continuous (equal-length sides, equal-measure inner angles) or irregular (not limited to congruent angles or sides). The regular, convex decagon is a subtle and also elegant shape, with 10 exterior angle of 36°, 10 inner angles that 144°, and 10 vertices (intersections of sides).


Because that is a complicated shape come make, the regular, convex decagon is popular with coins (like those native Australia, Belize and Hong Kong). Rarely often, rarely decagons should simply have 10 sides closing in a space, however the lengths of your sides have the right to vary greatly.

Concave and Convex Decagons

Most polygons deserve to be convex or concave. Convex decagons bulge outward, through no inner angle better than 180°. Concave decagons have indentations, developing interior angles better than 180°. That is why the rundown of a five-pointed star is a concave decagon; the has 5 interior angles each of i beg your pardon is far greater 보다 180°.


So much all the decagons questioned -- regular, irregular, concave, and also convex -- share the exact same properties:

10 sides10 vertices10 interior angles

Simple and complicated Decagons

Decagons deserve to be straightforward or complex. A simple decagon has no political parties crossing themselves. A an easy decagon adheres to all the typical "rules" of polygons.


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

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

Regular decagonConvex decagonSimple decagon

So, to it is in absolutely exact (and possibly a little fussy) you can define this figure as a regular, convex, straightforward decagon:

Decagon Shapes

Below are number of decagons. See, without looking in ~ the identifying information, if you can determine whether every is continual or irregular, convex or concave, straightforward 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, straightforward decagona concave, an easy decagona complicated decagona concave, simple decagon

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

Lesson Summary

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