How to Find The Perimeter

What is the Perimeter of Shape?

Imagine you just got a puppy for your birthday. Since the puppy will need to run and play in your backyard, we will need to build a fence around your backyard. To do this, we will need to know how much fencing to buy.

This is where the perimeter is needed. We will need to find the perimeter of your yard first before we can start building the fence. Then we will know how much fencing to buy.

Let’s see what perimeter is. When we measure the border of a shape, we can get
the perimeter of it. That is because the perimeter is the measurement of the boundary of a shape.

So, it is helpful to identify the shape first. Then we will need to know the measurement of each side.

Back to your yard. Let’s say that your yard is in the shape of a rectangle. We really don’t need to measure each side of the rectangle since a rectangle has two equal sides.

Below is a picture of a backyard that has a rectangle shape like your yard. We measure the long side of the rectangle, and it measures 30 feet, and the short side of the rectangle measures 15 feet. This is all we need to find the perimeter.

Example

One side of the rectangle has a measurement of 30 feet, and the shorter side of the rectangle measures 15 feet. The other two sides are also 30 feet and 15 feet. At this point, we have the name of the shape which is the rectangle.

The other part that we need is the measurements for all of the sides. In this case, we have the measurements of the sides that we need. Then we can work the problem.

The good news is that we can find the perimeter of any shape, and it is pretty easy to do. We can find the perimeter of triangles, rectangles, squares, and, yes, even circles.

Circles are a little more difficult when it comes to finding the perimeter, but we will talk about that later.

We must know how long each side of the shape is. If we don’t know or can’t find how long a side is, then we are in trouble. The only way to find the measurement of an unknown side is to cross your fingers that it is equal to another side, and we have the measurement of that equal side.

Once we have the lengths of each side, we are good to go!

FACT: Many people have to find the perimeter almost every time they are fencing in a yard.

Finding the Perimeter of Shapes with Sides

Now, I promised you that it would be easy to find the perimeter of a shape. It is rather easy to find the perimeter of most shapes. Unfortunately, the circle requires a few more steps to find its perimeter.

The formula of the square, triangle, rectangle, and really any other shape (that is not a circle) is quite simple. You add the lengths of each side together. That total is the perimeter.

So, the formula for most shapes is:

Side + side + side + side = perimeter

Example

See if you can work on this problem.

You are wrapping a present. You want to cut just enough ribbon to go around the square box. Below shows the measurement for one side of the box.

You may see that we only have the measurement for one side of our square. Don’t worry. That is all we need. Every side on a square is equal in length. That is what makes it a square.

So, we only need to know one side of the square. In this case, it is 24 inches. That means that every side is 24 inches. A square has 4 sides. So, we can set up the problem below to find the perimeter of it.

24 + 24 + 24 + 24 = 96 inches.

The perimeter of the square is 96 inches.

We need 96 inches of ribbon. We can wrap that amount of ribbon around the box. It will be just enough ribbon to wrap one time around this box.

That was quite easy, but not all shapes use this formula for the perimeter.

The circle is a different story.

Finding the Perimeter of a Circle

Now, the formula for the perimeter for a circle is a little different. Let’s first look at
the reason. If someone asked you the question:

“How many sides does a circle have?”

What would you say?

Actually, a circle doesn’t have any sides. So, the answer is zero. That is why we can’t use the same perimeter formula for a circle.

Instead of needing to know the measurement of a side, you need to know the radius or diameter of the circle. Look at the circle below. The dot is in the center of the circle.

The line from the dot to the edge of the circle is called the radius. The line that goes all the way across the circle and passes through that center dot is called the diameter.

You need either the radius or the diameter of the circle to find its perimeter.

Once you know either the amount for the radius or the diameter, you are ready to calculate the perimeter of the circle. You only need the radius or the diameter. The radius is actually half of the diameter.

Therefore, you can calculate the perimeter of the circle if you have one or the other. If you prefer to use the diameter formula, but you only have the radius, then you can double the radius measurement to get the diameter measurement.

The formula for the perimeter of a circle is:

$$\mathrm{πr}\times2$$ if you have the radius or $$\mathrm{πd}$$ if you have the diameter.

So, what do these symbols mean? We have already learned that “r” means radius which is the line that goes from the middle of the circle to the edge of it.

The “d” means diameter which is the line that goes straight through the center of the circle from one edge to the other edge.

You may have never seen this symbol $$\mathrm\pi$$. It is called pi. Don’t get too excited. It is not the kind that you eat like apple or cherry. Instead, it represents a certain amount which is 3.14.

So, you just need to plug in those numbers and amounts into the formula to get the perimeter.

Example

Look at this example to see how to plug in those numbers.

To work the problem, we will use 3.14 because that is what the symbol $$\mathrm\pi$$ represents.

Next, we need to know which two numbers to multiply first. We will use the order of operations rules to know which numbers to solve first.

In this case, both operations are multiplying, so the order of operations is not important, but it is always a good idea to get into the habit of following this rule.

So, we will multiply starting from the left and moving to the right. Therefore, we will multiple 2 times 3.14 that represents pi.

This is equal to 6.28. The last step is the multiply 6.28 with 5 which is the radius. The answer is 31.4.

After a little calculating, the perimeter for that circle is 31.4 inches.

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