This lesson goes over how to find the perimeter of a rectangle and a square. Here are some definitions to help you with this lesson:

• Perimeter: The length of the outside edge.
• Rectangle: A four sided shape whose opposite sides are the same length and all the corners form right angles.

• Square: A four sided rectangle where all sides are the same length.

Real World Application

A right angle is also a 90 degree angle. We won’t go into angles in this course but it is good to have a basic understanding of this vocabulary.

Video Source (04:22 mins) | Transcript

Perimeter is the sum of the outside edge lengths. For rectangles and squares we can simplify this because some of the side lengths are the same. (L = length, W = width)

Perimeter of a rectangle: \(L + L + W + W = 2L + 2W\) (By combining like terms.)

Perimeter of a square: \(W + W + W + W = 4W\)

Additional Resources

• Khan Academy: Introduction to Perimeter (3:20 mins; Transcript)

Practice Problems

1. The top of a pizza box forms a square where each side is 35 cm. Find the perimeter of the square defined by this pizza box. (
   Video Solution

   x

   Solution: 140 cm
   Details:
   

   
   (Video Source | Transcript)
   )
2. A rectangular swimming pool has a length of 20 ft and a width of 12 ft. Find the perimeter of the rectangle defined by this swimming pool. (
   Solution

   x

   Solution: 64 ft
   Details:
   Here is a rectangle that represents the swimming pool in this question.
   
   
   The opposite sides of a rectangle are the same lengths. This means there are actually two sides that are \({\color{Blue}20}\) feet long and two sides that are \({\color{Green}12}\) feet long.
   
   
   Since all the sides are measured using the same units, all we need to do to find the perimeter of the pool is to add together the lengths of all four sides.
   
   \({\color{Green}12} + {\color{Green}12} + {\color{Blue}20} + {\color{Blue}20} = 64\)
   
   Another way to add up the sides of the pool is to multiply the lengths of the sides by 2 and add them together since there are two sides of each length.
   
   \(2 ({\color{Green}12}) + 2 ({\color{Blue}20}) = {\color{Green}24} + {\color{Blue}40} = 64\)
   
   So the total perimeter of the pool is 64 feet.
   )
3. The borders for the state of Colorado form a rectangle that measures about 360 miles long and 280 miles wide. Find the perimeter of the rectangle defined by this state. (
   Video Solution

   x

   Solution: 1280 mi
   Details:
   

   
   (Video Source | Transript)
   )
4. A rectangular flag has a length of 150 cm and a width of 120 cm. Find the perimeter of the rectangle defined by this flag. (
   Solution

   x

   Solution:
   540 cm
   )
5. The cover of a book has a length of 5 in and a width of 8 in. Find the perimeter of the rectangle defined by this book cover. (
   Solution

   x

   Solution: 26 in
   Details:
   The sides of this book have all been measured in inches.
   
   
   The opposite sides of a rectangle have the same lengths. This means this rectangle has two sides that measure \({\color{Green}5}\)inches and two sides that measure \({\color{Blue}8}\) inches.
   
   
   The total perimeter is found by adding up the lengths of all the sides.
   
   \({\color{Green}5} + {\color{Blue}8} + {\color{Green}5} + {\color{Blue}8} = {\color{Green}5} + {\color{Green}5} + {\color{Blue}8} + {\color{Blue}8} = 26\)
   
   (The order in which we add up the sides doesn’t matter.)
   
   Another way to think of this is to multiply each side length by 2 since there are two sides of the same length for each length, and then add these together.
   
   \(2 ({\color{Green}5}) + 2 ( {\color{Blue}8} ) = {\color{Green}10} + {\color{Blue}16} = 26\)
   
   The perimeter of the rectangle defined by this book is 26 inches.
   )
6. A basketball court is rectangular in shape with a length of 29 m and a width of 15 m. Find the perimeter of the rectangle defined by this court. (
   Solution

   x

   Solution:
   88 m
   )

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