Mathematics college student from countries as far-flung together Australia, Belize and Hong Kong may have actually everyday contact with decagons, because those nations have used the 10-sided shape in their coins. Many of us, though, only encounter decagons in math class and when feeling particularly patriotic.

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Decagons are Polygons

Decagons belong come the family members of two-dimensional shapes called polygons. Polygons acquire their surname from Greek, meaning "many-angled," because all polygons have actually multiple inner angles. Lock close in a two-dimensional space using just straight sides.


How plenty of Sides go A Decagon Have?

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

Properties that Decagons

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

10 sides10 interior angles10 vertices

Decagon Angles

In many decagons, the sum of interior angles will be 1,440°, yet that is not 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 interior angles that 144°, summing come 1,440°


Drawing a decagon takes no skill; simply attract 10 heat segments the connect, and you have actually it. Illustration a regular, convex decagon, however, takes real skill, since each inner angle need to be 144°, and also all sides should be equal in length.

Drawing a concave decagon is actually reasonably easy: make a five-pointed star and fill that in. The is the star that appears 50 time on ours country"s flag, and the summary of such a pentagram (five-pointed star) is a decagon. That method you check out a many decagons anytime friend are near our flag:


Be careful to know the difference in 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, with 10 inner angles, and also 10 vertices i m sorry is wherein the political parties meet.A regular decagon has 10 equal-length sides and equal-measure inner angles. Each angle procedures 144° and also they all add up come 1,440°.An irregular decagon has sides and also angles that room not all same or congruent.A convex decagon bulges outward, through no interior angle higher than 180°.A concave decagon have actually indentations, producing interior angles greater than 180°.A simple decagon does not have any kind 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 have the right to be drawn as consistent (equal-length sides, equal-measure inner angles) or irregular (not minimal to congruent angle or sides). The regular, convex decagon is a subtle and elegant shape, v 10 exterior angle of 36°, 10 internal angles of 144°, and 10 vertices (intersections that sides).


Because it is a an overwhelming shape to make, the regular, convex decagon is famous with coins (like those from Australia, Belize and Hong Kong). Irregular decagons need to simply have actually 10 sides closing in a space, however 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 internal angle greater than 180°. Concave decagons have actually indentations, producing interior angles greater than 180°. The is why the overview of a five-pointed star is a concave decagon; that has 5 interior angles each of which is far greater 보다 180°.


So far all the decagons questioned -- regular, irregular, concave, and also convex -- re-superstructure the same properties:

10 sides10 vertices10 interior angles

Simple and facility Decagons

Decagons can be basic or complex. A basic decagon has no political parties crossing themselves. A straightforward decagon complies with all the conventional "rules" the polygons.


By contrast, a complicated decagon is self-intersecting. In cross its own sides, a facility decagon set off added interior spaces, however it is still stated to have actually only 10 sides, 10 internal angles, and 10 vertices. Due to the fact that it is so highly irregular and self-intersecting, a complicated decagon need not follow any kind of predictable rule about interior angle or their sums.

Notice the a single decagon have the right to fit right into several categories. The classic regular decagon meets every these requirements:

Regular decagonConvex decagonSimple decagon

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

Decagon Shapes

Below are several decagons. See, without looking at the identifying information, if you deserve to determine whether each is regular or irregular, convex or concave, simple or complex. Psychic to surname 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, straightforward decagona concave, simple decagona complicated decagona concave, basic decagon

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

Lesson Summary

Now that you have actually studied this lesson, you are able come recognize and define a decagon, state the identifying nature of every decagons, and also the identifying properties of consistent decagons. Girlfriend are likewise able to identify as decagons the stars on the U.S. Flag, and also identify the differences in between regular and irregular decagons; straightforward and facility decagons; and concave and also convex decagons.