Perimeter
Definition
Definition Perimeter
The perimeter of a shape is the total length around its outside edge.
To find the perimeter, imagine walking around the shape like it’s a park. Count the number of unit lengths along each side as you go.
Example
Find the perimeter of the red shape:
The perimeter is 8 units.
Perimeter of Common Shapes
Method Finding a Polygon’s Perimeter
To find the perimeter of any polygon (a shape with straight sides), add up the lengths of all its sides.
Proposition Perimeter Formulas
| Name | Shape | Perimeter |
| Triangle |  | \(a + b + c\) |
| Rectangle |  | \(l+w+l+w= (2\times l) + (2\times w) \) |
| Square |  | \(s+s+s+s=4\times s\) |
| Circle |  | \(2\times \pi \times r\) |
Example
Find the perimeter of the rectangle:
This is a rectangle with length \(l = 14\) m and width \(w = 7\) m. Using the formula for the perimeter of a rectangle:$$\begin{aligned}[t]P &= (2\times l) + (2\times w) \\&= (2 \times 14) + (2 \times 7) \\&= 28 + 14 \\&= 42 \, \mathrm{m}\end{aligned}$$So, the perimeter is \(42\) meters.
Perimeter of Composite Figures
Definition Composite Figure
A composite figure is a shape made up of two or more simple shapes, like triangles, rectangles, or squares, combined together.
Method Finding the Perimeter of a Composite Figure
To find the perimeter of a composite figure:
- Identify all the outer sides of the shape.
- Add the lengths of these outer sides together to find the total perimeter.
Example
Find the perimeter of the composite figure:
\(P=\)
+
\(\begin{aligned}[t]P &= \textcolor{colordef}{3\times 4 \mathrm{~cm}} + \textcolor{colorprop}{2\times 5 \mathrm{~cm}}\\P &= 22 \mathrm{~cm}\\\end{aligned}\)