How to Draw a Decagon for Kids TUTORIAL

Mathematics students from countries as far-flung as Australia, Belize and Hong Kong may have everyday contact with decagons, since those countries take used the 10-sided shape in their coins. Nigh of u.s.a., though, only run into decagons in mathematics class and when feeling particularly patriotic.

Decagons Are Polygons

Decagons belong to the family of two-dimensional shapes called polygons. Polygons get their name from Greek, meaning "many-angled," considering all polygons have multiple interior angles. They close in a ii-dimensional infinite using but direct sides.

How Many Sides Does A Decagon Have?

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

Backdrop of Decagons

For a polygon to be a decagon, it must have these identifying backdrop:

1. 10 sides
2. x interior angles
3. 10 vertices

Decagon Angles

In many decagons, the sum of interior angles will be $\mathrm{1,440}°$, but that is not an identifying property considering complex decagons will non have that sum.

Regular decagons take two additional identifying backdrop:

1. x exterior angles of $36°$, summing to $360°$
2. ten interior angles of $144°$, summing to $\mathrm{ane,440}°$

Drawing a decagon takes no skill; simply depict 10 line segments that connect, and you lot accept information technology. Drawing a regular, convex decagon, even so, takes real skill, since each interior bending must exist $144°$, and all sides must be equal in length.

Drawing a concave decagon is really fairly easy: make a v-pointed star and make full it in. That is the star that appears 50 times on our state's flag, and the outline of such a pentagram (five-pointed star) is a decagon. That means yous see a lot of decagons someday you are near our flag:

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

Decagon Definitions

• A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides see.
• A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures $144°$ and they all add together up to $\mathrm{1,440}°$.
• An irregular decagon has sides and angles that are not all equal or congruent.
• A convex decagon bulges outward, with no interior angle greater than $180°$.
• A concave decagon have indentations, creating interior angles greater than $180°$.
• A unproblematic decagon does not have any sides that cantankerous or intersect.
• A complex decagon has cocky-intersecting sides, is complex, and highly irregular.

Regular and Irregular Decagons

All polygons can be drawn as regular (equal-length sides, equal-mensurate interior angles) or irregular (not restricted to congruent angles or sides). The regular, convex decagon is a subtle and elegant shape, with 10 outside angles of $36°$, ten interior angles of $144°$, and 10 vertices (intersections of sides).

Because information technology is a challenging shape to make, the regular, convex decagon is popular with coins (similar those from Commonwealth of australia, Belize and Hong Kong). Irregular decagons must simply have 10 sides endmost in a space, just the lengths of their sides can vary greatly.

Concave and Convex Decagons

Nearly polygons tin be convex or concave. Convex decagons bulge outward, with no interior angle greater than $180°$. Concave decagons take indentations, creating interior angles greater than $180°$. That is why the outline of a five-pointed star is a concave decagon; information technology has five interior angles each of which is far greater than $180°$.

So far all the decagons discussed -- regular, irregular, concave, and convex -- share the same properties:

• 10 sides
• x vertices
• x interior angles

They also share one more property: their interior angles always add to $\mathrm{1,440}°$. That is non the case with the side by side category of decagons: circuitous.

Simple and Complex Decagons

Decagons can be elementary or complex. A elementary decagon has no sides crossing themselves. A simple decagon follows all the conventional "rules" of polygons.

Past contrast, a complex decagon is self-intersecting. In crossing its own sides, a complex decagon sets off additional interior spaces, but it is however said to have only 10 sides, x interior angles, and 10 vertices. Because it is so highly irregular and self-intersecting, a complex decagon need not follow any predictable rule well-nigh interior angles or their sums.

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

• Regular decagon
• Convex decagon
• Simple decagon

So, to be absolutely accurate (and mayhap a bit fussy) you can depict this figure as a regular, convex, simple decagon:

[insert drawing of regular decagon]

Decagon Shapes

Beneath are several decagons. Run across, without looking at the identifying information, if you tin can determine whether each is regular or irregular, convex or concave, simple or complex. Remember to name all the attributes, in example a shape fits more than one category.

In order, those decagons are:

1. a regular, convex, simple decagon
2. a concave, simple decagon
3. a complex decagon
4. a concave, uncomplicated decagon

Did you correctly place all of them by all their qualities? We sure promise and so!

Lesson Summary

At present that you have studied this lesson, you are able to recognize and define a decagon, state the identifying properties of all decagons, and the identifying properties of regular decagons. Y'all are also able to identify equally decagons the stars on the U.S. flag, and identify the differences between regular and irregular decagons; simple and complex decagons; and concave and convex decagons.

Next Lesson:

Ratios and Proportions

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How to Draw a Decagon for Kids TUTORIAL

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