# 8.10: Polygon Classification

**At Grade**Created by: CK-12

**Practice**Polygon Classification

Mustafa's parents are beekeepers. He watches them tend to the bees and get the honey. He sees patterns in the structure of the beehives and he notices that each hive tends to have the same little holes. The holes appear to have six sides. What type of polygon is Mustafa seeing?

In this concept, you will learn how to classify polygons.

### Classifying Polygons

A **polygon** is a closed figure made up of lines and angles. A polygon is classified by its number of sides.

Here is a table with information on some of the different types of polygons.

Polygon Name |
Polygon |
Number of Angles and Sides |
Sum of Interior Angles |
---|---|---|---|

triangle | 3 | \begin{align*}180^\circ\end{align*} | |

rectangle/square | 4 | \begin{align*}360^\circ\end{align*} | |

pentagon | 5 | \begin{align*}540^\circ\end{align*} | |

hexagon | 6 | \begin{align*}720^\circ\end{align*} | |

heptagon | 7 | \begin{align*}900^\circ\end{align*} | |

octagon | 8 | \begin{align*}1,080^\circ\end{align*} | |

nonagon | 9 | \begin{align*}1,260^\circ\end{align*} | |

decagon | 10 | \begin{align*}1,440^\circ\end{align*} |

Polygons have similar names. Look at the name for the shape that has eight angles and sides. It is called an octagon. In octagon, "oct" means “eight.” An octopus, for example, has eight arms. In pentagon, "pent" means “five,” so this is a shape with five sides.

Now take a look at the column on the right. Each kind of polygon has a different sum of its interior angles. For instance, the three angles in a triangle always add up to \begin{align*}180^\circ\end{align*}, and the four angles in a quadrilateral always add up to \begin{align*}360^\circ\end{align*}.

Let’s look at an example of classifying a polygon.

Identify the polygon below.

First, count the number of sides.

6 sides.

Then refer to the table.

The polygon is a hexagon.

The answer is hexagon.

### Examples

#### Example 1

Earlier, you were given a problem about Mustafa and the beehives.

He sees that the tiny holes appear to have six sides. What type of polygon is Mustafa seeing?

First, write the number of sides.

6 sides

Then refer to the table.

The polygon is a hexagon.

The answer is hexagon.

#### Example 2

Identify the polygon below.

First, count the number of sides.

9 sides.

Then refer to the table.

The polygon is a nonagon.

The answer is nonagon.

**Use what you have learned to identify each polygon.**

#### Example 3

The sum of the interior angles is \begin{align*}180^\circ\end{align*}.

First, refer to the table to see the number of sides that correspond to the sum of the interior angles.

3 sides

Then, name the polygon.

Triangle

The answer is triangle.

#### Example 4

It has seven sides.

First, note the number of sides.

7

Then, refer to the table.

The shape is a heptagon.

The answer is a heptagon.

#### Example 5

It has five sides and five angles.

First, note the number of sides.

The shape has five sides.

Then refer to the table.

The shape is a pentagon.

The answer is a pentagon.

### Review

Identify the polygons in the diagram. Then find the measures of the unknown angles.

Answer true or false for each of the following questions.

- A rhombus is always a square.
- A parallelogram has opposite sides that are parallel.
- A rectangle is a type of parallelogram.
- Squares, rectangles and rhombi are parallelograms with four right angles.
- A trapezoid has four right angles.
- A trapezoid has one pair of parallel sides.

Determine whether or not each image is a polygon. If yes, write polygon, if no, write not a polygon.

- A square tile on a floor

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.10.

### Resources

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
---|---|---|---|

Show More |

Term | Definition |
---|---|

Concave |
A concave polygon has at least one interior angle greater than 180 degrees. A common way to identify a concave polygon is to look for a "caved-in" side of the polygon. |

Convex |
A convex polygon contains no interior angles greater than 180 degrees. |

Diagonal |
A diagonal is a line segment in a polygon that connects nonconsecutive vertices |

Exterior angles |
An exterior angle is the angle formed by one side of a polygon and the extension of the adjacent side. |

Interior angles |
Interior angles are the angles inside a figure. |

Parallelogram |
A parallelogram is a quadrilateral with two pairs of parallel sides. |

Polygon |
A polygon is a simple closed figure with at least three straight sides. |

Quadrilateral |
A quadrilateral is a closed figure with four sides and four vertices. |

Rectangle |
A rectangle is a quadrilateral with four right angles. |

Regular Polygon |
A regular polygon is a polygon with all sides the same length and all angles the same measure. |

Rhombus |
A rhombus is a quadrilateral with four congruent sides. |

Square |
A square is a polygon with four congruent sides and four right angles. |

Vertices |
Vertices are points where line segments intersect. |

Equilateral |
A polygon is equilateral if all of its sides are the same length. |

### Image Attributions

In this concept, you will learn how to classify polygons.

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