What is Perimeter? - Definition & Formula

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Lesson Transcript
Instructor: Jennifer Beddoe
In mathematics, the perimeter is the distance around a two-dimensional shape. The formula for finding the perimeter of certain shapes will be discussed in this lesson, and there will be some examples to help you understand how to calculate the perimeter.

Definition

The word perimeter means a path that surrounds an area. It comes from the Greek word 'peri,' meaning around, and 'metron,' which means measure. Its first recorded usage was during the 15th century. In mathematics, the perimeter refers to the total length of the sides or edges of a polygon, a two-dimensional figure with angles. When describing the measurement around a circle, we use the word circumference, which is simply the perimeter of a circle.

There are many practical applications for finding the perimeter of an object. Knowing how to find the perimeter is useful for finding the length of fence needed to surround a yard or garden, or the amount of decorative border to buy to cover the top edges of a room's walls. Also, knowing the perimeter, or circumference, of a wheel will let you know how far it will roll through one revolution.

Perimeter Formulas: Some Terms

The basic formula for finding the perimeter is just to add the lengths of all the sides together. However, there are some specialized formulas that can make it easier, depending on the shape of the figure. Before we begin, let's define some abbreviations, or variables, we'll be using in our formulas.

We'll represent the perimeter, the value we're trying to find, with a capital P. For a shape that has all of its sides the same length, we'll use an s to represent a side. We can also use s with a number after it to represent sides of shapes that have more or less than four sides, which may be the same or different lengths. We can write these variables like this: s1, s2, s3, etc.

For a shape that has two of its opposite sides the same as each other and its other two opposite sides the same as each other but different from the first two sides, we'll need two variables. We'll call the longer of the two distances 'length' and the shorter of the two distances 'width.' We'll represent length with an l and width with a w, as follows:

• l = length
• w = width

Finding the Perimeter for a Square

Each side of a square has the same length, so we can use our abbreviation s to represent a side. A square has four sides, so we can find its perimeter by finding the length of any side and multiplying it by 4. We write the formula this way: P = 4s.

In the picture shown here, each side of the square has a length of 6 feet. Using our formula, P = 4s, we plug in the value of the length of one side for s: P = 4 * 6 ft. 6 * 4 = 24, so the perimeter of our square is 24 feet.

Finding the Perimeter for a Rectangle

A rectangle has right angles like a square does, but it has two longer sides that are the same (length) and two shorter sides that are the same (width). If we know the length of one side and the width of another, we can add them together and multiply by 2. We write the formula this way: P = 2(l + w).

To find the perimeter of the rectangle shown here, we need to have the length of one of the longer sides and the width of one of the shorter sides. We see from the labels that the length is 6 and the width is 3.

Starting with our formula, P = 2(l + w), we then substitute 6 for the l and 3 for the w: P = 2(6 + 3). Adding 6 and 3 equals 9, so our equation now looks like this: P = 2(9). Multiplying 2 times 9 gives us 18, which is the perimeter of the rectangle.

Finding the Perimeter of a Triangle

A triangle has three sides, which may be the same or different lengths. The easiest way to find the perimeter is to just add the sides together. We can write the formula like this: P = s1 + s2 + s3. For a triangle, we often represent the three sides with the letters a, b, and c, so we can also write the formula as P = a + b + c.

For the triangle shown here, we start with our formula and then plug in the lengths of each side in place of the variables representing the sides. Now, we add up the lengths of the sides. Adding 4 + 8 + 11 = 23, so the perimeter of our triangle is 23 centimeters.

Finding the Perimeter of a Polygon

A triangle is a polygon with only three sides. To find the perimeter of a polygon, add up the lengths of all the sides, just as you did for the triangle. The difference here is that the polygon shown here has more sides than the triangle did.

This polygon, called a pentagon, is a polygon with five sides, so we write the formula this way: P = s1 + s2 + s3 + s4 + s5. Now, we substitute the lengths of the sides for the variables representing them: P = 5 + 4 + 2 + 7 + 1. We add up the sides: 5 + 4 + 2 + 7 + 1 = 19, so we write our result this way: P = 19.

One thing to remember when finding the perimeter of an object is that you can only add lengths that have the same unit. If one side of an object is in inches and another is in feet, you must convert either inches to feet or feet to inches before adding. If no units are given, you can assume they are the same. Now, we're going to work through a couple of example problems on perimeters.

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