Quadrilateral Area Formulas

Square, rectangle, rhombus, parallelogram, trapezoid — all in one reference

Reviewed by [email protected], Geometry Calculator Developer & Online Math Educator Last updated May 8, 2026

A quadrilateral is any 4-sided polygon. The area formula depends on the specific type — but every quadrilateral has its own one-line formula. The most general approach for an irregular quadrilateral with known coordinates is the Shoelace formula.

The Formulas

Name Formula Notes
Square A = s² s = side length. Equivalent: A = ½ × d² where d is the diagonal.
Rectangle A = l × w l = length, w = width.
Parallelogram A = b × h b = base, h = perpendicular height.
Rhombus A = ½ × d₁ × d₂ d₁, d₂ = the two diagonals.
Trapezoid (Trapezium) A = ½ × (b₁ + b₂) × h b₁, b₂ = parallel bases, h = perpendicular height.
Kite A = ½ × d₁ × d₂ Diagonals are perpendicular.
Cyclic Quad (Brahmagupta) A = √((s−a)(s−b)(s−c)(s−d)) For quadrilaterals inscribed in a circle. s = (a+b+c+d)/2.
Irregular (Shoelace) A = ½ × |Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)| For any quadrilateral with known vertex coordinates.
Perimeter (any) P = a + b + c + d Sum of all four sides.

Worked Examples

Example 1: Rectangle 8 × 5

  1. A = 8 × 5 = 40 unit²
  2. P = 2(8 + 5) = 26 units

Example 2: Trapezoid with bases 10 and 6, height 4

  1. A = ½ × (10 + 6) × 4 = ½ × 16 × 4 = 32 unit²

Example 3: Rhombus with diagonals 12 and 8

  1. A = ½ × 12 × 8 = 48 unit²

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