Quadrilateral Calculator
Calculate area and perimeter of quadrilaterals using multiple methods
Calculate Quadrilateral Properties
Four Sides and Two Opposite Angles
Quadrilateral Results
Method: Bretschneider's formula
Formula: Area = √[(s-a)(s-b)(s-c)(s-d) - abcd·cos²((α+β)/2)]
Example Calculation
Irregular Quadrilateral Example
Sides: a = 350 ft, b = 120 ft, c = 280 ft, d = 140 ft
Opposite angles: α = 70°, β = 100°
Semiperimeter: s = (350 + 120 + 280 + 140) / 2 = 445 ft
Calculation Steps
1. Calculate (s-a)(s-b)(s-c)(s-d) = 95 × 325 × 165 × 305 = 1,555,721,250
2. Calculate abcd·cos²((α+β)/2) = 350×120×280×140×cos²(85°) = 113,142,432
3. Area = √(1,555,721,250 - 113,142,432) = √1,442,578,818
Area ≈ 37,981 ft²
Types of Quadrilaterals
Square
4 equal sides, 4 right angles
Rectangle
Opposite sides equal, 4 right angles
Rhombus
4 equal sides, opposite angles equal
Parallelogram
Opposite sides parallel and equal
Trapezoid
One pair of parallel sides
Kite
Two pairs of adjacent equal sides
Formula Quick Reference
Bretschneider's Formula
A = √[(s-a)(s-b)(s-c)(s-d) - abcd·cos²((α+β)/2)]
Diagonal Formula
A = (d₁ × d₂ × sin(θ)) / 2
Bimedian Formula
A = m₁ × m₂ × sin(θ)
Shoelace Formula
A = ½|Σ(x₍ᵢ₎y₍ᵢ₊₁₎ - x₍ᵢ₊₁₎y₍ᵢ₎)|
Understanding Quadrilateral Calculations
What is a Quadrilateral?
A quadrilateral is a polygon with four edges (sides) and four vertices (corners). The word comes from the Latin "quadri" (four) and "latus" (side). Quadrilaterals can be simple (non-self-intersecting) or complex (self-intersecting).
Classification
- •Convex: All interior angles less than 180°
- •Concave: One interior angle greater than 180°
- •Simple: No self-intersecting edges
- •Complex: Self-intersecting edges
Calculation Methods
Bretschneider's Formula
Most general formula for any quadrilateral. Requires four sides and two opposite angles. Named after German mathematician Carl Anton Bretschneider.
Diagonal Method
Uses the lengths of both diagonals and the angle between them. Particularly useful for kites and rhombuses.
Bimedian Method
Uses bimedians (lines connecting midpoints of opposite sides) and the angle between them.
Coordinate Method
Shoelace formula using vertex coordinates. Works for any simple polygon.