General Quadrilateral
Calculator and formulas for calculating the properties of a general quadrilateral
This function calculates various properties of a general quadrilateral.
To calculate, enter the lengths of 3 sides and the two angles that connect these sides. Then click on the 'Calculate' button.
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Formulas for the general quadrilateral
Diagonal (e)
\(\displaystyle e =\sqrt{a^2+b^2-2ab·cos(β)} \)
Diagonal (f)
\(\displaystyle f =\sqrt{b^2+c^2-2bc·cos(γ)} \)
Area (A)
given a, b, c, d, e, f
\(\displaystyle A=\frac{\sqrt{4e^2f^2-(b^2+d^2-a^2-c^2)^2}}{4}\)
given a, b, c, d, α, δ
\(\displaystyle A=\sqrt{(s-a)(s-b)(s-c)(s-d)-abcd·cos^2\left(\frac{α+γ}{2} \right)} \)
\(\displaystyle s=\frac{a+b+c+d}{2} \)
Perimeter (P)
\(\displaystyle P=a+b+c+d\)
Angle (α)
\(\displaystyle α=arccos\left(\frac{a^2+d^2-f^2}{2ad} \right)\)
Angle (δ)
\(\displaystyle δ=360°-α-β-γ\)
Side (d)
\(\displaystyle d=\sqrt{c^2+e^2-2ce·cos(γ_2)}\)
\(\displaystyle γ_2=γ-γ_1\)
\(\displaystyle γ_1=arcos\left(\frac{b^2+e^2-a^2}{2be}\right)\)
Square • Rectangle • Golden Rectangle • Rectangle to Square • Rhombus, given varios parameter • Rhombus , given diagonal e, f • Parallelogram, given 2 sides and angle • Parallelogram area, given side and height • Trapezoid • Cyclic Quadrilateral • General Quadrilateral • Concave Quadrilateral • Arrowhead Quadrilateral • Crossed Square • Frame • Kite, given 2 diagonal and distance • Kite Area, given 2 diagonal • Half Square Kite • Right Kite"
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