Finding the perimeter

Finding the perimeter of a shape means that you are looking for the distance around the outside of that shape.

Example #1

Find the distance around for the following irregular polygon


Distance around = 5 inches + 4 inches + 2 inches + 3 inches + 6 inches = 20 inches

Example #2

Find the distance around for the following trapezoid


Distance around = 5 inches + 8 inches + 4 inches + 3 inches = 20 inches

Example #3

Find the distance around the following triangle


Distance around = 5 inches + 4 inches + 2 inches = 11 inches

Example #4

Find the distance around the following rectangle


Distance around = 3 inches + 3 inches + 6 inches + 6 inches = 18 inches

Example #5

Find the distance around the following square


distance around = 5 inches + 5 inches + 5 inches + 5 inches = 20 inches
You can get the same answer by doing 4 × 5 = 20

Finding the perimeter of a more interesting shape such as a house by counting unit squares

How would you find the perimeter of the shape below looking like a house?

Remember that the perimeter is the distance around the shape. Therefore, you will need to ignore some of the lines and some of the shapes.

Some of these lines or shapes are there to distract or confuse you. For example, you need to ignore the door and the two lines inside the house. Below, we show the length of 3 sides.

The only thing that is missing is the length of the line shown with a question ?

To find it, you need to notice that this line is the hypotenuse of the right triangle. Therefore, you can use the Pythagorean theorem to find it.

c² = a² + b²

c² = 3² + 5²

c² = 9 + 25

c² = square root of 34

c = 5.83 

Perimeter = 10 + 8 + 8 + 5.83 + 5.83 = 37.66

Finding the perimeter when one or more side lengths are missing.

Find the perimeter of the shape below that has two missing sides.

We need to find these two missing sides before we can find the perimeter. Were you able to see which sides are missing? If not we show them below a red line and a green line.

To find the missing sides, you need to make the following important observations.

x = 4 cm + 3.5 cm = 7.5 cm

3 cm + y = 7 cm

3 cm - 3 cm + y = 7 cm  - 3 cm

y = 4 cm

Perimeter = 3 cm + 3.5 cm  + 4 cm + 4 cm + 7 cm + 7.5 cm = 29 cm