What Is Perimeter Used For? (10 Real Life Uses Of Perimeter)

Perimeter is used often in mathematics for word problems in geometry and optimization problems in calculus. Perimeter is vital for finding the surface area of some objects, but it also has numerous applications in real life.

So, what is perimeter used for?  Perimeter is used for various applications in business, housing, construction, gardening, and crafts. For example, a gardener uses perimeter to find out how much fence to use to close in a rectangular garden. A painter uses perimeter to help figure out how much paint to buy for a job.

Of course, perimeter has many more applications in real life: from area optimization to buildings, perimeter plays a role.

In this article, we’ll talk about 10 important real life uses of perimeter.  We’ll also give some examples so you can see the numbers at work.

Let’s get started.

What Is Perimeter Used For? (10 Uses Of Perimeter)

Perimeter has many applications in business, housing, construction, gardening, and crafts, and other disciplines.  Here are 10 ways that perimeter is used in real life:

• Area Optimization (limited materials)
• Border Lengths For States & Countries
• Building A Shed
• Gardening (length of fence needed to enclose an area)
• Molding Above Doors & Windows
• Picture Frames
• Surveying (Real Estate Property Lines)
• Paint or Wallpaper For A Room
• Running On A Track (distance around)
• Upholstery (Furniture Repair)

Let’s take a closer look at each of these in turn, starting with business.

Area Optimization

Perimeter helps us to minimize the use of materials when we want a shape with a certain area.  You can solve some of these problems by graphing, but others may require calculus.

Example: Using Perimeter To Optimize Area

Let’s say that you want a rectangular cardboard box with an area of 36 square inches.  We want to find the dimensions (length and width) that minimize the perimeter.

This will minimize the amount of cardboard used to make the box, thus reducing waste.

First, we will name variables: call the dimensions x (length) and y (width).

Next, come up with an equation for total perimeter of the box.  Since each side is counted twice, we get a perimeter of:

• P = 2x + 2y

Then, we come up with an equation to represent a constraint on the dimensions.  Specifically, the area must be 36 square inches.  The area of a rectangle with sides x and y is xy, so we get:

• xy = 36

Now, we must minimize the perimeter by using the constraint.  To make the problem easier, we will rewrite P = 2x + 2y so that it is a function of one variable instead of two.

Solving xy = 36 for y, we get:

• y = 36 / x

Substituting y into P = 2x + 2y, we get:

• P = 2x + 2y
• P = 2x + 2(36 / x)
• P(x) = 2x + (72 / x)

We want to find the value of x that minimizes the function P(x) above.  We can graph the function (shown below) or we can use calculus to find the minimums by using derivatives.

The first derivative is

• P’(x) = 2 – (72 / x²)

The first derivative is zero when:

• P’(x) = 0
• 2 – (72 / x²) = 0
• 2 = 72 / x²
• 2x² = 72
• X² = 36
• x = +/- 6

Since x is a length, we want the positive value, so x = 6.

We can verify that x = 6 is a minimum for the perimeter function by taking the second derivative:

• P’’(x) = 144 / x³

Which is positive when x = 6, meaning we have a minimum at that point.

Since x = 6, we must also have y = 6, since y = 36 / x.

So, the box should have a length of 6 inches and a width of 6 inches to have an area of 36 square inches.  We can find the volume of the box if we multiply the area by the height.

Border Lengths

The perimeter of a shape tells us the distance you would need to walk to go all the way around the shape.  So, the perimeter of a state or country tells us the length of a border.

You can also find the part of a state or country’s border that touches an ocean.  This can give you an idea of how much of the border is susceptible to tidal waves, tsunamis, and storms from the ocean.

Building A Shed

If you want to build a wooden shed, you need to know how much lumber to buy.  The perimeter of the shed is one thing you will need to calculate before you begin working.

The perimeter of the shed tells you the board-length that you will need for the walls.  For example, if the shed has a height of 8 feet, a length of 10 feet, and width of 12 feet, then the perimeter is:

• Perimeter = 2*length + 2*width
• Perimeter = 2*10 + 2*12
• Perimeter = 44 feet

So you would need 44 feet of board that is 8 feet tall to build the perimeter of the shed.

Gardening

When building a fence for a garden to keep animal pests out, you will need to know how much fencing to buy.  The perimeter will tell you this.

For example, if the garden is 20 feet long by 30 feet wide, then the perimeter is:

• Perimeter = 2*length + 2*width
• Perimeter = 2*20 + 2*30
• Perimeter = 100 feet

So you would need 100 feet of fence to close in the entire garden.  Of course, you will also need one or two gates so you can get in and out easily.

Molding

In construction, molding is used around doors and windows as decoration.  To find out how much molding you will need for a window, you will need to calculate the perimeter of a window.

For a door, you will need to calculate the perimeter without the bottom part (since molding does not go at the bottom of a door).

Picture Frames

When making picture frames, you need to know how much material you need to go all the way around the picture.  As before, the perimeter is twice the length plus twice the width.

For example, if the picture is 8 inches long by 10 inches wide, then the perimeter is:

• Perimeter = 2*length + 2*width
• Perimeter = 2*8 + 2*10
• Perimeter = 36 inches

So, a piece of material (wood, plastic, metal) that is 36 inches long (3 feet) will give you enough material to make one frame.