Perimeter

Definition

Perimeter ($P$) is the total distance around the boundary of a closed two-dimensional figure.

Why It Matters

Perimeter is the most fundamental measure of a system’s “footprint.” Whether you are calculating the amount of fencing needed or the amount of heat loss from a building’s envelope, the boundary is the point of interaction.

Core Concepts

• Polygon Perimeter: The sum of the lengths of all sides.
  • Triangle: $P = a+b+c$
  • Rectangle: $P = 2(b+h)$
  • Square/Rhombus: $P = 4s$
  • Regular $n$-gon: $P = ns$
  • How to read: “The perimeter P is equal to the sum of the side lengths a, b, and c; the perimeter P is equal to two times the sum of the base b and the height h; the perimeter P is equal to four times the side length s; and the perimeter P is equal to the number of sides n times the side length s.”
  • Meaning: Perimeter is total boundary length—add all sides (or multiply side count by side length for regular polygons).
• Circumference: The perimeter of a circle ($C = 2\pi r$).
  • How to read: “The circumference C is equal to two times pi times the radius r.”
  • Meaning: Distance around a circle—one full rotation of radius $r$.

Connected Concepts

• Semiperimeter
• Area of a Triangle
• Area of Quadrilaterals
• Circle Fundamentals