Polygons Concave Regular

Lesson 6: Classifying Polygons

by Micah Davis

​Plane Figures

​A polygon is a closed plane figure with at least 3 sides all formed by line segments. Each endpoint of each side intersects another side's endpoints. These endpoints are called vertices (singular form: vertex).

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​Each endpoint can only intersect two other sides.

​Convex and Concave

​Convex polygons have no sides that contain a point on the interior of the polygon.

​

​Concave polygons are nonconvex polygons.

​Classifying Polygons

Polygons are classified by their number of sides. You can see in the table to the right the different names of each polygon. Polygons with more than ten sides are usually called n-gons where n is the number of sides it has (for example, a 27 sided polygon is called a 27-gon). ​12-sided polygons are called dodecagons.

Multiple Choice

A 3 sided polygon is called a...

• triangle

• quadrilateral

• pentagon

• trigon

Multiple Choice

Is the polygon concave or convex?

• concave

• convex

​Finding Missing Lengths

​In the image to the right, we are looking for the length of the regular hexagon given the perimeter of 30 inches. We can set the problem up like this:

​s + s + s + s + s + s = 30

​When simplified, we get:

​6s = 30

​And solved:

​s = 5 inches

​Finding Missing Lengths

​Given a regular pentagon with one side of (3x + 6) inches and another side of (4x - 2) inches, find the lengths of the sides. We can set up the sides equal to each other:

​(3x + 6) = (4x - 2)

​Then, subtract 3x from each side to begin solving for x:

​6 = x - 2

​Then, solve for x:

​x = 8

​To find the sides of the polygon (which are all equal since it is regular), we plug x back in to one of the expressions for a side:

​3x + 6 -> 3(8) + 6

​Then, simplify the expression 3(8) + 6 to find the sides are 30 inches long.

Multiple Choice

Given a regular quadrilateral with one side with the length (3x - 4) inches and another length of (2x + 9) inches, find the lengths of the sides.

• 35 inches

• 23 inches

• 13 inches

• 43 inches