Perimeter Calculator
Calculate perimeter or circumference of common 2D shapes with formulas.
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Perimeter Formulas for Common Shapes
Perimeter is the total distance around the boundary of a 2D shape. It is measured in linear units (cm, m, ft, in, etc.). For a circle, the perimeter is called the circumference.
Rectangle and Square
Rectangle: P = 2 × (length + width). Square: P = 4 × side. A 6×4 rectangle has perimeter 2×(6+4) = 20.
Triangle
P = a + b + c (sum of all three sides). No formula simplification unless it's equilateral (P = 3×side) or isosceles.
Circle (Circumference)
C = 2πr = πd, where r is radius and d is diameter. For r=5: C = 2π×5 ≈ 31.42 units. The circumference is the distance around the circle.
Regular Polygons
P = n × s, where n is the number of sides and s is the side length. Regular pentagon (5 sides, side=4): P = 20. Regular hexagon (6 sides, side=4): P = 24.
Applications
Perimeter is used for fencing (amount of material to surround a yard), framing (picture frame length), flooring borders, and track layouts. It is the one-dimensional measurement complementing two-dimensional area.
Worked Example: Fencing a Garden
A garden is shaped like a trapezoid with parallel sides of 12 m and 8 m, and two non-parallel sides each 5 m. How much fencing is needed?
Perimeter = sum of all four sides = 12 + 8 + 5 + 5 = 30 m. You would need 30 metres of fencing. If fencing costs $12 per metre, the total cost is 30 × $12 = $360.
Perimeter Formulas at a Glance
| Shape | Formula | Example (result) |
|---|---|---|
| Rectangle | 2(l + w) | 2(10 + 6) = 32 |
| Square | 4s | 4 × 7 = 28 |
| Triangle (scalene) | a + b + c | 3 + 4 + 5 = 12 |
| Circle | 2πr | 2π × 5 ≈ 31.42 |
| Regular Pentagon | 5s | 5 × 6 = 30 |
| Regular Hexagon | 6s | 6 × 4 = 24 |
Frequently Asked Questions
P = 2(8+5) = 2×13 = 26 units.
Circumference is the perimeter of a circle: C = 2πr. For radius 6: C = 12π ≈ 37.70 units.
Perimeter is the distance around the boundary (linear, 1D). Area is the space enclosed (squared, 2D).
P = 3 × 7 = 21 units.
P = 6 × 5 = 30 units. All regular polygons: P = number of sides × side length.
Yes. A rectangle 1×9 and a rectangle 3×7 both have perimeter 20, but areas of 9 and 21 respectively. Among all shapes with the same perimeter, a circle encloses the greatest area — this is known as the isoperimetric inequality.
P = 2(a + b), where a and b are the lengths of the two pairs of parallel sides. For a parallelogram with sides 8 and 5: P = 2(8 + 5) = 26 units. Note that only the side lengths matter, not the angles or height.