Concave Quadrilateral calculator and formulas

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.

Concave Quadrilateral

Input

Side a

Side b

Side c

Angle β

Angle γ

Decimal places

Results

Side d

Diagonal e

Diagonal f

Area A

Perimater U

Angle α

Angle δ

Formulas for the concave quadrilateral

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 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

\( A=\sqrt{\frac{a+d+f}{2}·\left(\frac{a+d+f}{2}-a\right)·\left(\frac{a+d+f}{2}-d\right)·\left(\frac{a+d+f}{2}-f\right)} \)

\( +\;\sqrt{\frac{b+c+f}{2}·\left(\frac{b+c+f}{2}-b\right)·\left(\frac{b+c+f}{2}-c\right)·\left(\frac{b+c+f}{2}-f\right)} \)

Concave Quadrilateral calculator

Calculate a concave quadrilateral

Formulas for the concave quadrilateral

Diagonal e

Diagonal f

Side d

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