Have you ever designed something and discovered an error in your plan? Well, look at what happened to Keith.

Keith began working on a design for a sign to advertise the opening of the skatepark. He didn't want to make it ordinary, so he chose a pentagon as the shape of the sign.

Keith drew it out and began to work on the lettering. When he was finished, he held up the sign and noticed that the bottom line of the pentagon was a different length from the other lines. The other four lines of the pentagon were all 2 feet in length, while the bottom line measured 2.5 feet.

Is this still a pentagon? Why?

**This Concept is all about regular and irregular polygons. At the end of the Concept, you will know how to identify the pentagon that Keith has drawn.**

### Guidance

Now that you have been introduced to the different types of polygons, it is time to learn about classifying polygons. All polygons can be classified as ** regular** or

**polygons. You have to understand the difference between a regular or irregular polygon to classify each shape. Let’s learn how we can tell the difference between them.**

*irregular*
**What is a regular polygon?**

A regular polygon is a polygon where all of the side lengths are equal and all of the angle measures are equal. In other words, the polygon is an equilateral polygon where all the side lengths are *congruent*, and an equiangular polygon where all the angles are *congruent*.

This triangle is a regular triangle. All three side lengths are congruent and all three angles are congruent. Here is an example of an irregular polygon.

By counting the sides, you can see that this is a five sided figure. It is a pentagon. However, the sides are not congruent. Therefore, it is an *irregular* pentagon.

**Irregular polygons have side lengths that are not congruent.**

Now it’s time for you to practice. Name each figure as a regular or irregular polygon.

#### Example A

**Solution: Regular Polygon**

#### Example B

**Solution: Irregular Polygon**

#### Example C

An octagon with all sides measuring 4 centimeters.

**Solution: Regular polygon**

Here is the original problem once again.

Keith began working on a design for a sign to advertise the opening of the skatepark. He didn't want to make it ordinary, so he chose a pentagon as the shape of the sign.

Keith drew it out and began to work on the lettering. When he was finished, he held up the sign and noticed that the bottom line of the pentagon was a different length from the other lines. The other four lines of the pentagon were all 2 feet in length, while the bottom line measured 2.5 feet.

Is this still a pentagon? Why?

This figure is still a pentagon, but it is not a regular pentagon.

To be a regular pentagon, all of the side lengths would need to be equal in length.

Because one side is longer than the other four, this is an irregular pentagon.

However, it still has five sides, so it is still considered a pentagon.

### 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

- Regular Polygon
- polygon with all sides congruent

- Irregular Polygon
- a polygon where all of the side lengths are not congruent

- Congruent
- exactly the same or equal

### Guided Practice

Here is one for you to try on your own.

Jessie's new bedroom is square in shape. She measures one of the walls and finds that it is 12 feet long. She measures another wall and finds that it is 10 feet long. The other two walls are also different lengths.

Is Jessie's room a square?

Is it a regular polygon or an irregular polygon?

**Answer**

Jessie's room can not be a square because all of the walls are different lengths. It is also irregular in shape for this reason. Jessie's room is a quadrilateral because it has four walls, but is not a regular polygon.

### Video Review

James Sousa, Introduction to Polygons

James Sousa, Classifying Polygons

### Practice

Directions: Based on each description, determine whether the polygon is regular or irregular.

1. A quadrilateral with all sides equal to 5 cm and all right angles.

2. A pentagon with different side lengths.

3. A square.

4. A rectangle.

5. An octagon with one side that is 8 cm and the other sides congruent to that side. All angles are congruent.

6. A heptagon with seven congruent sides and angles.

7. A hexagon with six congruent angles.

8. A hexagon with the following side lengths: 4 m, 5 m, 7 m, 5 m, 4 m and 7 m.

9. A pentagon with five congruent angles.

10. True or false. A figure can be a polygon and be regular or irregular.

Directions: Identify each polygon below.

11. a

12. b

13. c

14. d

Directions: Now tell whether each is regular or irregular.

15. a

16. b

17. c

18. d