Perimeter of a Rectangle

  1. Video
  2. What Makes a Rectangle a Rectangle?
  3. Perimeter of a Rectangle Formulas
  4. How to Find the Perimeter of a Rectangle
  5. Word Problems
  6. Examples

What Makes a Rectangle a Rectangle?

A rectangle is a two-dimensional polygon with four straight sides. It has opposite sides congruent and parallel. That means it will have two lengths and two widths.

A Rectangle's Perimeter

Perimeter is the distance around the sides of a polygon.

Perimeter of a Rectangle Formulas

To calculate perimeter in general, just add up the lengths of all the straight sides of a polygon, from a triangle up to a 100-gon (a hectogon). For a rectangle, that means adding four sides:

P = a + b + c + d

Where P is the perimeter and a, b, c, and d are the lengths of the four sides.

Rectangles are interesting, though, because they really have two pairs of two sides; two lengths, and two widths. So instead of writing out P = a + b + c + d you can combine terms and multiply:

P = 2 × (length + width)

Perimeter is always expressed in the same linear measurement used for the lengths of sides.

Perimeter of a Rectangle Formulas

How to Find the Perimeter of a Rectangle

Here we have a rectangle with four vertices, D, U, C, K.

Rectangle DUCK

Sides DU and KC are congruent and parallel. Sides DK and UC are also congruent and parallel. That is why you only see two dimensions on the drawing. If Side KC is 17 feet, then you know side DU is 17 feet. Since side DK is 8 feet, you know side UC is 8 feet.

Use either formula:

How To Find The Perimeter of a Rectangle

P = a + b + c + d

P = 17 + 8 + 17 + 8

P = 50

Let's try the other formula:

P = 2 × (length + width)

P = 2 × (17 + 8)

P = 2 (25)

P = 50

See, when calculating the perimeter of DUCK using either formula, you cannot fowl it up!

Perimeter of Rectangles Word Problems

Because the formulas for rectangle perimeter are so easy, they often form the foundation for word problems. Here's one:

Cindy is decorating his Science Fair poster and wants to put a decorative ribbon around the edges. The ribbon has tiny pictures of methane molecules on it. His poster, "CH4 Comes From Cows and More," is 36" long and 24" wide. How many feet of methane molecule ribbon does Cindy need?

That is a classic (if a little nutty) word problem, throwing in distractors and real mathematics. Boil it down to the task, ignoring the rest:

  1. Poster 36" long and 24" wide
  2. Perimeter for ribbon, expressed in feet

P = a + b + c + d

P = 36 + 24 + 36 + 24

Or, with our second formula:

Perimeter of Rectangles Word Problems

P = 2 × (length + width)

P = 2 × (36 + 24)

P = 2 (60)

P = 120" = 10'

Cindy needs 10 feet of methane molecule ribbon.

Another Perimeter of Rectangle Example

You may find a perimeter problem using algebra, where you have to find unknowns. Here's one of those:

Rectangle BRAG

Rectangle BRAG has a perimeter of 96 cm. Side BR is 3x - 4 long, and side BG is x + 5 wide. What are its measurements?

You can still use both formulas, but you have to simplify along the way. Combine like terms; subtract 2 from both sides, and divide:

P = a + b + c + d

P = 3x - 4 + x + 5 + 3x - 4 + x + 5 = 96

P = (3x + x + 3x + x) + (- 4 + 5 - 4 + 5) = 96

P = 8x + 2 = 96

8x = 94

x = 11.75 cm

Now let's try with our second formula:

P = 2 × (length + width)

P = 2 (3x - 4 + x + 5) = 96

P = 2 (3x + x - 4 + 5) = 96

P = 2 (4x - 1) = 96

P = 8x - 2 = 96

8x = 94

x = 11.75 cm

Plug 11.75 cm into the x values, and check:

3x - 4

3 (11.75) - 4 = 31.25

&

x + 5

11.75 + 5 = 16.75

First formula:

Perimeter of Rectangle Example

P = a + b + c + d

P = 31.25 + 16.75 + 31.25 + 16.75

P = 96 cm

Now let's try with our second formula:

P = 2 × (length + width)

P = 2 (31.25 + 16.75)

P = 2 (48)

P = 96 cm

Do not lose your unit of measure as you work through the problem; all perimeter is measured in the same linear unit you used for each side.

Lesson Summary

Working hard through this lesson, you are now able to define perimeter, recall and apply two formulas for finding the perimeter of a rectangle and solve word problems involving perimeter of rectangles.

P = a + b + c + d

P = 2 × (length + width)

Maybe some other civilizations may have sprung up around circles, ovals, and spheres, but our world is dominated by rectangles, squares (which are special rectangles), and the three-dimensional forms you can build with them. Homes are essentially rectangular prisms with rectangular windows and doors. Schools are building-block assemblages of rectangular prisms. Knowing how to find the perimeter of a rectangle is a helpful skill in everyday life.

Next Lesson:

What is a Triangle?

What you learned:

After working your way through this lesson and video, you will learn to:

  • Define perimeter
  • Recall and apply two formulas for finding the perimeter of a rectangle
  • Solve word problems involving perimeter of rectangles
Instructor: Malcolm M.
Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.
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Ashburn, VA

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