Perimeter Formulas by Shape
| Shape | Formula |
|---|---|
| Square | P = 4 × s |
| Rectangle | P = 2 × (l + w) |
| Circle | P = 2π × r = π × d |
| Triangle | P = a + b + c |
| Equilateral Triangle | P = 3 × s |
| Parallelogram | P = 2 × (a + b) |
| Trapezoid | P = a + b + c + d |
| Rhombus | P = 4 × s |
| Regular n-gon | P = n × s |
What is Perimeter?
Perimeter is the total distance around the outside of a 2D shape. For straight-sided shapes, it's the sum of all side lengths. For circles, it's called the circumference. Perimeter is measured in units of length (cm, m, in, ft), while area is measured in square units.
Real-World Uses
- Fencing: How much fencing to enclose a garden or yard
- Framing: Length of frame material needed for a picture or window
- Track length: Distance around a running track or field
- Baseboards: Length of baseboard/skirting for a room perimeter
- Construction: Length of foundation footing for a building footprint
Frequently Asked Questions
What is the difference between perimeter and area?
Perimeter is the length of the boundary around a shape (1D measurement, in linear units). Area is the amount of 2D space inside the shape (in square units). A 10m × 10m square has a perimeter of 40m but an area of 100m².
Can two shapes have the same perimeter but different areas?
Yes. A 1×9 rectangle and a 3×3 square both have a perimeter of 20 units, but areas of 9 and 9 — in this case equal. But a 1×9 vs a 4×5 both perimeter 20, areas 9 vs 20. Among all shapes with the same perimeter, the circle encloses the maximum area (isoperimetric theorem).
How do I find the perimeter if I only know the area?
You need to know the shape. For a square: side = √area, then P = 4×side. For a circle: r = √(area/π), then P = 2πr. For other shapes, you need at least one more measurement.