Perimeter of Polygons

The perimeter is the total distance around the outside of a shape. Imagine you are an ant walking exactly along the edge of a shape until you get back to where you started. The total distance you walked is the perimeter!

How to Find the Perimeter

To find the perimeter of any polygon, simply add up the lengths of all its sides.

Example: A triangle has sides that are $3\text{ cm}$, $4\text{ cm}$, and $5\text{ cm}$. What is its perimeter? $P = 3 + 4 + 5 = 12\text{ cm}$

Shortcuts for Rectangles and Squares

For some shapes, you don't have to add every single side one by one. You can use quick math shortcuts!

Rectangles: A rectangle has two equal lengths and two equal widths. You can use this formula: $P = 2 \times (\text{length} + \text{width})$

Example: Find the perimeter of a rectangle that is $8\text{ cm}$ by $5\text{ cm}$. $P = 2 \times (8 + 5) = 2 \times 13 = 26\text{ cm}$

Squares: A square has four equal sides. Just multiply the length of one side by $4$: $P = 4 \times \text{side length}$

Example: If a square has a side length of $6\text{ cm}$, its perimeter is $4 \times 6 = 24\text{ cm}$.

Finding a Missing Side Length

Sometimes you know the total perimeter, but one side length is a mystery. To find it, add up the sides you do know, and subtract that sum from the total perimeter.

Example: A shape has a total perimeter of $24$. Three of its sides are $5$, $7$, and $6$. What is the length of the missing fourth side?

1. Add the known sides together: $5 + 7 + 6 = 18$
2. Subtract that number from the total perimeter: $24 - 18 = 6$

The missing side is $6$!