Concave Quadrilateral calculator
Calculator and formulas for a concave quadrilateral
This function calculates various parameters of a concave quadrilateral.
In a concave quadrilateral, one of the two diagonals lies outside the figure.
To calculate, enter the lengths a, b and c and the angles beta (β) and gamma (γ). Then click on the 'Calculate' button.
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Description
A concave quadrilateral has four vertices connected by four side lines. The word “concave” comes from the Latin word “concavus,” which means “curved inward” in English. A concave quadrilateral has at least one corner point curved inwards, so that it is inside the surface.
In a concave square, one of the two diagonals lies outside the figure.
Formulas
Diagonal e
\(\displaystyle e =\sqrt{a^2+b^2-2·a·b·cos(β)} \)
Diagonal f
\(\displaystyle f =\sqrt{b^2+c^2-2·b·c·cos(γ)} \)
\(\displaystyle β_1 =β- arccos\left(\frac{b^2+f^2-c^2}{2·b·f}\right) \)
Side length d
\(\displaystyle d=\sqrt{a^2+f^2-2·a·f·cos(β_1)}\)
Angle α
\(\displaystyle α=arccos\left(\frac{a^2+d^2-f^2}{2·a·d}\right) \)
Angle δ
\(\displaystyle δ=360°-α-β-γ \)
Perimeter P
\(\displaystyle P=a+b+c+d \)
Area A
\( A=\sqrt{\frac{a+d+f}{2}·\left(\frac{a+d+f}{2}-a\right)·\left(\frac{a+d+f}{2}-d\right)·\left(\frac{a+d+f}{2}-f\right)} \)
\(\ \ \ \ +\;\sqrt{\frac{b+c+f}{2}·\left(\frac{b+c+f}{2}-b\right)·\left(\frac{b+c+f}{2}-c\right)·\left(\frac{b+c+f}{2}-f\right)} \)
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