Have you ever visited a sculpture garden?

*Courtesy of Martin Fuchs*

Marc, Isaac and Isabelle continue to work on their design for the skate park. Isabelle loves art and thinks that adding some sculpture to the entrance of the skate park could be cool way to integrate art into the design. Marc and Isaac agree and the three decide to visit a sculpture garden to get ideas. Once they decide on what they want to create, they hope that Mr. Craven, the art teacher, will help them create it with some other classmates.

Upon visiting the sculpture garden, the three notice immediately that there are many different shapes in each sculpture.

Their favorite sculpture is pictured above. Isabelle liked the three dimensional aspect of the sculpture, but did not like that it was all made of triangles.

“Let’s design one with all kinds of polygons,” Marc suggests as they head home.

“That’s a great idea! Which ones should we use?” Isabelle asks.

“What is a polygon anyway?” Isaac interrupts.

Marc and Isabelle look at him. Isaac has not been paying attention in math class.

**Before Marc and Isabelle fill in Isaac, what do you know about polygons? Can you define them? Which ones should the trio use in their sculpture? Pay attention in this Concept and you will learn all about polygons.**

### Guidance

This Concept begins talking about ** polygons** in specific detail. Previously we worked with triangles and with quadrilaterals. Triangles and quadrilaterals are also polygons; we just haven’t been describing them in this way yet. This Concept will help you to understand how to identify polygons as well as learn some valuable information about them. Polygons are everywhere in the world around us and you will be working with polygons in many ways for a long time.

**What is a polygon?**

**A polygon is a simple closed figure formed by three or more segments.** A triangle is a polygon and a quadrilateral is a polygon too. Here are three pictures of polygons.

**Polygons**

These figures are not polygons. A polygon does not have a curve in it. The first two figures have curves in them. The third figure is not a closed figure. The last figure has sides that overlap. A polygon does not have sides that overlap.

There are several different types of polygons. Some of them you may have heard of before.

**What are some different types of polygons?**

1. **Triangle – has three sides**

2. **Quadrilateral – has four sides**

3. **Pentagon – has five sides**

4. **Hexagon – has six sides**

5. **Heptagon – has seven sides**

6. **Octagon – has eight sides**

7. **Nonagon – has nine sides**

8. **Decagon – has ten sides**

These polygons can be seen in real life all the time. Look at the following pictures and determine which polygon is pictured.

#### Example A

**Solution: Octagon**

#### Example B

**Solution: Pentagon**

#### Example C

**Solution: Hexagon**

*Courtesy of Martin Fuchs*

Here is the original problem once again.

Marc, Isaac and Isabelle continue to work on their design for the skatepark. Isabelle loves art, and thinks that adding some sculpture to the entrance of the skatepark could be cool way to integrate art into the design. Marc and Isaac agree and the three decide to visit a sculpture garden to get ideas. Once they decide on what they want to create, they hope that Mr. Craven, the art teacher, will help them create it with the help of some other classmates.

Upon visiting the sculpture garden, the three notice immediately that there are many different shapes in each sculpture.

Their favorite sculpture is pictured above. Isabelle liked the three dimensional aspect of the sculpture, but did not like that it was all made of triangles.

“Let’s design one with all kinds of polygons,” Marc suggests as they head home.

“That’s a great idea! Which ones should we use?” Isabelle asks.

“What is a polygon anyway?” Isaac interrupts.

Marc and Isabelle look at him. Isaac has not been paying attention in math class.

**Marc, Isabelle and Isaac want to design a sculpture of polygons. A polygon is a closed figure made up of at least three line segments.**

Once they fill Isaac in on how to define a polygon, the three students begin to list out different types of polygons.

Triangle

Square

Rectangle

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

**After a lot of negotiation, here is a rough sketch of their sculpture design. Can you identify each polygon?**

### Vocabulary

- Polygon
- A simple closed figure formed by three or more line segments.

- Pentagon
- five sided polygon

- Hexagon
- six sided polygon

- Heptagon
- seven sided polygon

- Octagon
- eight sided polygon

- Nonagon
- nine sided polygon

- Decagon
- ten sided polygon

### Guided Practice

Here is one for you to try on your own.

If you have a heptagon next to a nonagon, what is the sum of the sides?

**Answer**

A seven sided figure is a heptagon.

A nine sided figure is a nonagon.

\begin{align*}7 + 9 = 16\end{align*}

**There are sixteen sides between the two figures.**

### Video Review

James Sousa, Introduction to Polygons

James Sousa, Classifying Polygons

### Practice

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

1.

2.

3.

4.

5.

6.

7.

8. A square tile on a floor

Directions: For numbers 8 – 15, go back and use each figure in 1 – 7. Explain why it is or why it is not a polygon.

8.

9.

10.

11.

12.

13.

14.

15.