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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn the process you need to take to find the perimeter of polygons. You will also learn that there is a shortcut if your polygon is a regular polygon.

**Polygons**, flat shapes with straight sides, are very popular. Look around, and you are bound to see some. Your computer monitor is most likely a polygon, a rectangle to be exact. And just look at your window, too. That's also a polygon; probably a rectangle as well. And if you look down on a neighborhood from somewhere high up, you will see that each individual property has a fence or boundary around it, and that is most likely a polygon, too. Most properties have straight lines as boundaries all around.

If you can picture your polygon as a type of boundary, then your **perimeter** is the distance all around the shape. Another way to think of perimeter is the distance it will take to walk all around the shape or boundary.

When you are trying to find the perimeter, the length of each side is given to you. Usually, you are given a shape and then you see that each side has been labeled with a number. Because the perimeter is the distance all around, you would start with one side and work your way around the shape until you have added up all the numbers together. This sum is your answer for the perimeter.

Let's try finding the perimeter of this fenced-in field below.

If you look down from above, you can see that the fence makes a polygon shape since all of its sides are straight. You see horses enjoying themselves in the sun. You want to make a similar kind of field on your ranch, so you need to know how much fence is needed by finding the perimeter.

Because polygons come in all kinds of shapes with any number of sides, we need to make sure that we know the lengths of all of our sides. So, first, I look at my diagram, and I look for all my sides. I do see that they are all labeled with their lengths:

I have all the information I need to proceed. I pick the top side as my starting point, and I'm going to work my way clockwise around the shape. I need to add all of my numbers, so I start writing 8 + 5 + 5 + 8 + 11. I have all my sides written down.

Now, I double check by counting the amount of numbers I've written down and the amount of sides I have. I have five sides, and I have five numbers written down. My numbers are also correctly written down. So, now I can continue to find my answer by adding it all up. So, 8 + 5 + 5 + 8 + 11 = 37. But wait, what are my measuring units? Well, since the problem didn't specify units, I'm going to leave the number as is for an answer of 37.

If the problem gave a type of measuring unit, I would make sure that my answer had the same. So, if I was given feet, my answer would have feet in it as well. If I was given meters, my answer would have meters in it.

Here comes the shortcut. If you have a regular polygon, a polygon whose sides and angles are all the same length, then you can use a shortcut to find the perimeter. And what is this shortcut? This one requires multiplication. All you need to know is the length of one side since all of them are the same. Instead of adding the sides up one by one, all you would need to do is to multiply the length of one side by the number of sides. So, if I had a 10-sided regular polygon with sides that measured 3 inches, then my perimeter would be 10 * 3 = 30 inches. You can check this by adding up all the sides. You will find that it will give you the same answer.

A 12-sided regular polygon with sides that measured 8 feet would have a perimeter of 12 * 8 = 96 feet.

Remember, this shortcut only works for regular polygons. You will have to add up the sides one by one for any other type of polygon.

Now let's review what we've learned. We've learned that a **polygon**, a flat shape with straight sides, can be viewed as a boundary of sorts to help us in finding the perimeter. The **perimeter** is the distance all around the shape. We find the perimeter by adding up the length of all the sides of the polygon. If we view it as a fence, we just add up all the sides to find the total amount of fencing that was used to make the shape.

For most polygons, we add up the sides one by one. If we had a regular polygon, a polygon whose sides and angles are all the same, then we can simply multiply the length of one side by the number of sides to find the perimeter. Also, if the problem gives you a measuring unit, you have to use that measuring unit in your answer as well.

Upon completing this lesson, you may be prepared to:

- Recognize a polygon by its shape
- Find the perimeter of a polygon
- Use a shortcut method to find the perimeter of a regular polygon

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Geometry: High School15 chapters | 160 lessons

- Angles Formed by a Transversal 7:40
- Parallel Lines: How to Prove Lines Are Parallel 6:55
- Using Converse Statements to Prove Lines Are Parallel 6:46
- Constructing a Parallel Line Using a Point Not on the Given Line 5:15
- The Parallel Postulate: Definition & Examples 4:25
- What Are Polygons? - Definition and Examples 4:25
- Regular Polygons: Definition & Parts 6:01
- How to Find the Number of Diagonals in a Polygon 4:49
- Finding the Perimeter of Polygons 5:19
- Measuring the Angles of Triangles: 180 Degrees 5:14
- How to Measure the Angles of a Polygon & Find the Sum 6:00
- Go to High School Geometry: Parallel Lines and Polygons

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