Perimeter

Perimeter is the total distance around the outside of a two-dimensional shape — sum of all side lengths. For a circle, it goes by the special name circumference.

Common formulas:

• Rectangle: $P = 2l + 2w$
• Square: $P = 4s$
• Triangle: $P = a + b + c$
• Regular polygon (n sides): $P = n \cdot s$
• Circle (circumference): $C = 2\pi r = \pi d$

Perimeter is in linear units (cm, m, ft) — not squared like area. The distinction matters: doubling all sides doubles the perimeter but quadruples the area.

In real-world problems, perimeter shows up when you need to compute how much fencing for a garden, baseboard for a room, or framing for a window. The famous isoperimetric inequality says: among all shapes with a given perimeter, the circle encloses the maximum area.