Shape Perimeter Calculator

Perimeter: - units

Understanding Shape Perimeters

What is Perimeter?

Perimeter is the total length of the boundary of a two-dimensional shape. It represents the distance around the shape and is fundamental in geometry and real-world applications.

Circle: P = 2πr

Triangle: P = a + b + c

Rectangle: P = 2(l + w)

Regular Polygon: P = ns

where:

  • r = radius
  • a, b, c = side lengths
  • l = length, w = width
  • n = number of sides
  • s = side length

Advanced Perimeter Concepts

  • Isoperimetric Property: Maximum area for given perimeter
  • Perimeter Optimization: Minimizing boundary length
  • Fractal Perimeters: Infinite length in finite area
  • Jordan Curve Theorem: Simple closed curves
  • Perimeter-Area Relationships: Geometric inequalities
  • Discrete vs. Continuous Perimeters

Applications and Properties

Architectural Design

Building footprints and space planning

Landscape Architecture

Fencing and border calculations

Manufacturing

Material requirements and cutting patterns

Urban Planning

Property boundaries and zoning