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Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to see how the shapes that you grew up with are all related. Learn why the shapes of bricks, stars, and street blocks are considered polygons while the sun, moon, and rolling hills are not.

Polygons

Do you remember the very first shape you learned when you were little? It's okay if you don't, because I don't. But I do know that it was a polygon. What is a polygon? A polygon is a flat shape with straight sides. So, shapes such as triangles, squares and rectangles are all polygons. And I know one of those was the first shape I learned. I remember my first house drawing consisted of nothing but triangles, squares and rectangles. It was simple, but it turned out quite nice! When I say a polygon is flat, I mean that it is a shape you can draw on a flat piece of paper.

As the definition tells us, a polygon's sides must be straight. If any side is curved, then it's no longer a polygon. So, the moon, the sun and rainbows are not polygons because they are curved. Also, if you draw a shape and your end point is not the same as your start point, then you don't have a polygon either. The shape must be contained. There can't be any gaps.

Regular and Irregular Polygons

Polygons also fall into several categories. The categories I want to discuss with you are the regular and irregular categories. Regular polygons are those polygons whose sides and angles are all equal. These polygons look like they are reaching out to become a circle. Think of a stop sign, and you are seeing a regular polygon.

An irregular polygon is a polygon whose sides and angles are not all the same. Think of that stop sign again, and now think of pulling the shape in one direction. If you stretched it out so it did not look like a wannabe circle, then you would have an irregular polygon. Really, any polygon that doesn't look like it wants to be a circle is most likely an irregular polygon. But you can check that by looking to see if the sides and angles are all equal or not. If not, then it is irregular. If they are, then it is regular.

Concave and Convex Polygons

I also want to talk about the concave and convex categories. Convex polygons are polygons whose angles are all pointed outwards. Think of a kite, and you will see that all the angles look like they are pushed outwards by the structure of the kite. This makes the kite a convex polygon. Mathematically, all the angles of a convex polygon will measure less than 180 degrees.

A concave polygon, on the other hand, is a polygon with at least one angle that is pointed inwards. If you picture a rectangular brick colliding with a giant metal cone, the end result would be a concave polygon. You would have one angle that is greater than 180 degrees.

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Finally, we have the simple and complex categories. Simple polygons are polygons whose sides never cross each other. These shapes look like they could be fancy fences fencing off a fun shape. Boy, was that a tongue twister! All of your common shapes, like triangles and rectangles, are simple polygons because you can see that they create one boundary and are fencing off one area.

If you saw that your fence crossed itself somewhere and you had several boundaries or several fenced-off areas, then your polygon would be considered complex, meaning the polygon has sides that intersect. Draw the traditional star and you are looking at a complex polygon. Do you see how you had to cross over your own shape to draw the star? And do you see how the star creates several fenced-off areas instead of one common area?

Lesson Summary

We've learned quite a bit! We've learned that polygons can be categorized in all sorts of ways. We've also learned that polygons are everywhere. We've learned that a polygon is a flat shape with straight sides. A regular polygon has all its sides and angles equal. An irregular polygon does not have all sides and angles equal.

A convex polygon has all angles pointed outwards and less than 180 degrees. A concave polygon has at least one angle pointed inwards and measuring greater than 180 degrees. A simple polygon creates a fence around one area, while a complex polygon creates a fence with multiple areas.

Learning Outcomes

After you've completed this lesson, you'll be able to:

Define polygon

Differentiate between a regular and an irregular polygon

Describe what convex and concave polygons look like

Explain the difference in simple and complex polygons and provide an example of a complex polygon

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