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Perimeter of a Quadrilateral Calculator

Calculate quadrilateral perimeter using side lengths or coordinate vertices

Calculate Quadrilateral Perimeter

Formula

Perimeter = A + B + C + D

The perimeter is the sum of all four side lengths

Calculation Results

0.00
Perimeter (units)

Formula used: Perimeter = A + B + C + D = 0 + 0 + 0 + 0

Input Validation

⚠️ All side lengths must be greater than 0

Example Calculations

Rectangle

Given: Length = 8 cm, Width = 5 cm

Sides: A = 8, B = 5, C = 8, D = 5

Calculation: Perimeter = 8 + 5 + 8 + 5 = 26 cm

Square

Given: Side length = 6 cm

Sides: A = B = C = D = 6

Calculation: Perimeter = 6 + 6 + 6 + 6 = 24 cm

Quadrilateral from Coordinates

Vertices: A(0,0), B(4,0), C(5,3), D(1,3)

Side AB: √[(4-0)² + (0-0)²] = 4

Side BC: √[(5-4)² + (3-0)²] = √10 ≈ 3.16

Side CD: √[(1-5)² + (3-3)²] = 4

Side DA: √[(0-1)² + (0-3)²] = √10 ≈ 3.16

Perimeter: 4 + 3.16 + 4 + 3.16 = 14.32 units

Types of Quadrilaterals

Square
Four equal sides, four right angles
Rectangle
Opposite sides equal, four right angles
Parallelogram
Opposite sides parallel and equal
Rhombus
Four equal sides, opposite angles equal
Trapezoid
One pair of parallel sides
Kite
Two pairs of adjacent equal sides
Irregular Quadrilateral
No special properties

Perimeter Formulas

General Quadrilateral

P = a + b + c + d

Sum of all four sides

Rectangle

P = 2(l + w)

l = length, w = width

Square

P = 4s

s = side length

Distance Formula

d = √[(x₂-x₁)² + (y₂-y₁)²]

For coordinate method

Calculation Tips

All side lengths must be positive

Sum of any 3 sides > 4th side for validity

Coordinate method calculates exact distances

Perimeter is always the sum of all sides

Understanding Quadrilateral Perimeter Calculation

What is a Quadrilateral?

A quadrilateral is a closed two-dimensional shape with four straight sides, four vertices, and four angles. The perimeter is the total distance around the quadrilateral's boundary. Common quadrilaterals include squares, rectangles, parallelograms, trapezoids, rhombuses, and kites.

Types and Properties

  • Regular: Square (all sides and angles equal)
  • Rectangle: Opposite sides equal, all angles 90°
  • Parallelogram: Opposite sides parallel and equal
  • Irregular: No special symmetry properties

Calculation Methods

Four Side Lengths

Direct measurement method

P = a + b + c + d

Coordinate Vertices

Calculate distances from coordinates

d = √[(x₂-x₁)² + (y₂-y₁)²]

Special Cases

Optimized formulas for regular shapes

Square: P = 4s, Rectangle: P = 2(l+w)

Note: The coordinate method is most versatile and works for any quadrilateral shape, including irregular and concave quadrilaterals.

Validity Conditions

For a quadrilateral to exist with given side lengths, it must satisfy certain geometric constraints:

  • All sides must be positive lengths
  • Sum of any three sides must be greater than the fourth side
  • The longest side must be less than the sum of the other three

Real-World Applications

  • Architecture: Building floor plans and room layouts
  • Landscaping: Garden borders and fence calculations
  • Engineering: Structural design and material estimation
  • Graphics: Computer graphics and game development