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