How to Find Perimeter – Formulas for Common Shapes
How to Find Perimeter – Add the Outside Boundary Correctly
Perimeter is a boundary-length problem. The key is to identify the outside edge, add it once, and keep the units linear.
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What Is Perimeter?
Perimeter is the total length around the outside boundary of a 2D shape. Imagine walking once around the edge: the distance traveled is the perimeter.
Perimeter Formulas
| Shape | Formula |
|---|---|
| Rectangle | P=2L+2W=2(L+W) |
| Square | P=4s |
| Triangle | P=a+b+c |
| Regular n-gon | P=ns |
| Parallelogram | P=2(a+b) |
| Circle | C=2πr=πd |
Step-by-Step Method
- Trace the complete outside boundary.
- Identify every outside segment or use a shortcut formula for repeated equal sides.
- Convert all lengths to the same unit.
- Add each boundary length exactly once.
- Report the answer in a linear unit.
Irregular Shapes and Missing Sides
For an irregular polygon, add every exterior segment. Missing lengths can often be deduced because horizontal segments must balance overall widths and vertical segments must balance heights.
If a known total perimeter is given, an unknown side can be found by subtraction:
Worked Examples
Rectangle 8 m × 5 m
Square side 7 cm
Triangle sides 6, 9 and 11 ft
Regular hexagon side 4 in
Perimeter vs Area
A 6 m × 4 m rectangle has perimeter 20 m but area 24 m².
Practice Questions
Rectangle 12 ft × 9 ft
Answer: 2(12+9)=42 ft.
Regular octagon side 3 cm
Answer: 8×3=24 cm.
Questions People Ask
Open any question for a detailed explanation, not just a one-line answer.
How do you find perimeter?
Add the lengths of all outside edges. For shapes with repeated equal sides, use a shortcut formula such as P=4s for a square or P=2(L+W) for a rectangle.
Why is perimeter measured in normal units?
Perimeter is one-dimensional distance, so it uses linear units such as metres, feet or centimetres. Square units belong to area.
How do I find perimeter of an irregular shape?
Trace the outer boundary and add each exterior segment once. Do not include interior construction lines unless they are part of the actual boundary.
Can I find a missing side from perimeter?
Yes. Subtract the sum of all known boundary lengths from the total perimeter, provided the shape information is sufficient.
Is circumference the same as perimeter?
It is the same boundary concept applied to a circle. The special term is circumference, calculated with C=2πr or C=πd.
What is the difference between perimeter and area?
Perimeter measures boundary length; area measures the surface inside. They use different formulas and different unit dimensions.
Does a hole inside a shape affect perimeter?
It depends on what boundary the problem asks for. The external perimeter ignores an internal hole, but a total boundary-length problem may include both the outer edge and the hole’s boundary.
Where can I calculate perimeter for many shapes?
Use the Perimeter Calculator for rectangles, polygons, circular cases and more.
Related CalcTypes Resources
Methodology
This guide treats perimeter as total external boundary length, keeps unit dimensions explicit and separates circular circumference from area.