Rectangle Calculator

Area: -

Perimeter: -

Diagonal: -

Angles: -

Understanding Rectangles

What is a Rectangle?

A rectangle is a quadrilateral with four right angles. Key elements include:

  • Four right angles (90°)
  • Parallel opposite sides
  • Equal diagonal lengths
  • Rotational symmetry
  • Axial symmetry
  • Regular tessellation
  • Inscribed circle properties
  • Circumscribed circle properties
  • Golden ratio relationships

Key Formulas

Area:

A = l × w

Perimeter:

P = 2(l + w)

Diagonal:

d = √(l² + w²)

Angles:

All angles = 90°

Inscribed Circle Radius:

r = (l × w)/(l + w)

Circumscribed Circle Radius:

R = √(l² + w²)/2

Properties and Theorems

Geometric Properties

  • Opposite sides parallel and equal
  • Diagonals bisect each other
  • Diagonals equal in length
  • Two lines of symmetry
  • 180° rotational symmetry
  • Cyclic quadrilateral

Mathematical Properties

  • Area optimization
  • Isoperimetric inequality
  • Diagonal relationships
  • Trigonometric ratios
  • Vector representations
  • Coordinate geometry

Advanced Concepts

Calculus Applications

  • Optimization problems
  • Integration applications
  • Area under curves
  • Moment of inertia
  • Center of mass

Transformations

  • Rotations
  • Reflections
  • Translations
  • Dilations
  • Shear transformations

Real-World Applications

Architecture

  • Floor plans
  • Building design
  • Material estimation
  • Space optimization

Engineering

  • Manufacturing
  • Product design
  • Structural analysis
  • Material science

Technology

  • Screen design
  • UI/UX layouts
  • Digital imaging
  • Computer graphics