How to find the perimeter of a rectangle
Formula for the perimeter of a rectangle
The perimeter of a rectangle is the length of the boundary around the figure. You can find the perimeter of a rectangle by calculating the sum of the length of its four sides. Sometimes you’ll see the perimeter formula as
???P=2l+2w???
where ???l??? is the length of the rectangle, and ???w??? is the width of the rectangle.
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Examples of different ways to find the perimeter of a rectangle
Example
What is the perimeter of the rectangle?
You can find the perimeter by plugging the length and width that we’ve been given into the formula for the perimeter.
???P=2l+2w???
???P=2(20)+2(16)???
???P=40+32???
???P=72\text{ in}???
Remember that opposite sides of a rectangle are equal in length, so you could also find the perimeter by adding all of the side lengths together.
???P=20+16+20+16???
???P=72\text{ in}???
Sometimes you’ll be given the coordinates of a rectangle in a coordinate plane and asked to find the perimeter.
Example
A rectangle has one vertex at ???(1,1)??? and the opposite vertex (the vertex that’s connected to ???(1,1)??? by the diagonal) is at ???(8,7)???. What is the perimeter of the rectangle?
Drawing a sketch of the rectangle on the coordinate plane can help, so start by plotting the points.
Now draw in the rectangle.
Count the length of each side.
Add the side lengths to find the perimeter.
???P=6+7+6+7=26\text{ units}???
Other times you might need to perform a few calculations first before you can find the perimeter.
Remember that opposite sides of a rectangle are equal in length, so you could also find the perimeter by adding all of the side lengths together.
Example
What is the perimeter of the rectangle that has an area of ???96\text{ units}^2??? and a length of ???8??? units?
We need to know the dimensions of the rectangle in order to find its perimeter. We know the area is ???96\text{ units}^2??? and that is has a length of ???8??? units.
???A=lw???
???96=8w???
???w=12???
Now we can find the perimeter.
???P=2l+2w???
???P=2(8)+2(12)???
???P=40??? units
