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.
| 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. |
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