Polygons

The word polygon has Greek roots and means "many sides" or "many angles." A polygon is one of many plane shapes, which are defined as figures that are closed, flat, and 2-dimensional having length and width but no depth. Polygons are drawn using straight line segments that only meet at their endpoints. Shapes that don't close, are not straight line segments or do meet at points other than endpoints are not classified as polygons.

Take a look at the examples below of shapes that are and are not categorized as polygons:

It's good to note that while not all closed shapes are polygons, all polygons are closed shapes.

As you get to know more about polygons, it's good to learn their names and sides since they play a major role in how you can identify them. Every line segment in a polygon is known as a side. You can identify polygons by the number of line segments or sides they contain. For example, a pentagon is a polygon that has five sides ("penta" means "five" or "having five" and "-gon" refers to the number of sides or angles).

Here is a quick overview of polygon names and their sides:

Are you confused about the n -gon? It's less confusing than you might think. You might have noticed that, with the exception of the triangle and quadrilateral, all of the polygons listed above end in -gon. In truth, the triangle is also called a trigon, and the quadrilateral is also called a tetragon.

As mentioned previously, the suffix "-gon" refers to the side/angle while its prefix identifies the number. So, using the example of the pentagon, another way to write it would be 5-gon. If you want to write heptagon similarly, you can write it as 7-gon since it has seven sides. The triangle, or trigon, can be referred to as 3-gon for its three sides. And the quadrilateral, or tetragon, can be referred to as 4-gon. The term n -gon refers to a polygon with n sides. In this case, the n can refer to any integer.

Polygons fall under a variety of classifications based on their sides and angles. Here are six polygon classifications:

1. Regular polygons: All interior angles and sides of regular polygons are congruent (identical in form). An example of a regular polygon would be an equilateral triangle or square.
2. Irregular polygons: Sides and angles of irregular polygons are not congruent. Examples of irregular polygons include rectangles, parallelograms, and right triangles.
3. Convex polygons: Every interior angle of a convex polygon is less than 180 degrees. An example of a convex polygon would be a pentagon.
4. Concave polygons: At least one interior angle of a concave polygon is greater than 180 degrees. A five-pointed star is an example of a concave polygon.
5. Simple polygons: The sides of simple polygons don't intersect themselves and don't have holes. A square or hexagon is an example of a simple polygon.
6. Complex polygons: The sides of complex polygons cross over each other at least one time. A pentagram is an example of a complex polygon.

a. What is an example of a regular polygon?

A square

b. How many sides does a nonagon have?

9

c. A pentagon is an example of what type of polygon?

Convex polygon

d. What type of polygon could be referred to as a 6-gon?

Hexagon

e. Which polygon has 10 sides?

Decagon

f. Which polygons have interior angles and sides that are all congruent (identical in form)?

Regular polygons

g. Which polygon is also known as a tetragon or 4-gon?

Square

Graphing Polygons

Areas of Regular Polygons

Angles of Elevation and Depression

3rd Grade Math Flashcards

Basic Arithmetic Flashcards

Common Core: 3rd Grade Math Diagnostic Tests

3rd Grade Math Practice Tests

Polygons are shapes we encounter every day whether in the form of triangles, squares, or octagons. But correctly naming, identifying, and classifying them can sometimes be tough. The good news is your student doesn't have to struggle to grasp polygons. There are tutors eager to assist whether your student wants to simply gain a better understanding of polygons or would like to go over these plane shapes for an assignment or upcoming exam. If you want to learn more about the benefits of tutoring for your student, reach out to the Educational Directors at Varsity Tutors today.