How To Find The Perimeter of a Rectangle
Perimeter of a rectangle
Perimeter of a rectangle is total length of the rectangle's four sides.
Perimeter of a rectangle formulas
To calculate perimeter of a polygon, add up the lengths of all the straight sides. For a rectangle, that means adding four sides:
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 you can combine terms and multiply:
Perimeter is always expressed in the same linear measurement used for the lengths of sides.
How to find the perimeter of a rectangle
Here we have a rectangle with four vertices, D, U, C, K.
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:
Let's try the other formula:
See, when calculating the perimeter of DUCK using either formula, you cannot fowl it up!
Perimeter of rectangles example problem
Because the formulas for rectangle perimeter are so easy, they often form the foundation for word problems. Here's one:
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 either formulas, but you have to simplify along the way.
Combine like terms:
Subtract 2 from both sides:
Finally, divide by 8 and you get your answer:
Now, you can plug 11.75 cm into the x values, and see if you get 96 cm:
And...
Now plug these into the Perimeter formula that we started with:
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.