What is Perimeter?
The perimeter is the total distance around the outside boundary of a 2D shape. The word comes from the Greek perimetros meaning "around measure." Perimeter is always measured in linear units (cm, m, inches, feet) — not square units.
Think of perimeter as the length of fence needed to enclose a garden, or the length of ribbon needed to go around a picture frame.
Perimeter Formulas for All Common Shapes
| Shape | Formula | Variables |
|---|---|---|
| Square | P = 4s | s = side length |
| Rectangle | P = 2(l + w) | l = length, w = width |
| Triangle | P = a + b + c | a, b, c = all three sides |
| Circle | C = 2πr = πd | r = radius, d = diameter |
| Trapezoid | P = a + b + c + d | all four sides |
| Regular polygon (n sides) | P = n × s | n = sides, s = side length |
| Equilateral triangle | P = 3s | s = side length |
| Rhombus | P = 4s | s = side length |
Worked Examples
Example 1 – Garden Fencing
A rectangular garden is 15 m × 8 m. How much fencing is needed?
Example 2 – Running Track
A circular running track has diameter 80 m. What is one lap distance?
Example 3 – Picture Frame
A photo is 20 cm × 15 cm. How much ribbon is needed to border it?
Example 4 – Equilateral Triangle Sign
A triangular road sign has all sides 60 cm. Find the perimeter.
Perimeter vs Area — Key Distinction
These two measurements are commonly confused:
- Perimeter = boundary length (linear: cm, m) — how much fencing, edging, or border you need
- Area = enclosed surface (square: cm², m²) — how much paint, carpet, or turf you need
Important: Shapes with the same perimeter can have very different areas. A 5×5 square and a 1×9 rectangle both have perimeter 20, but areas of 25 and 9 respectively!
Real-World Applications
- Fencing: Calculate total fence length for gardens, sports fields, and properties
- Framing: Picture frames, door/window trim, baseboard length
- Track sports: Determining lap distances for running, cycling, horse racing
- Knitting & sewing: Calculating fabric borders, hemlines, binding
- Landscaping: Edging for garden beds, driveways, and pathways