Area of a general quadrilateral given four sides and two opposite anglesCreative Commons Attribution/Share-Alike License 3.0 (Unported)
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  1. Area of a quadrilateral given four sides and two diagonals. In this case it will be non-trigonometric Bretschneider's formula

{\displaystyle {\begin{aligned}F&={\tfrac {1}{4}}{\sqrt {4e^{2}f^{2}-(b^{2}+d^{2}-a^{2}-c^{2})^{2}}}\\&={\sqrt {(s-a)(s-b)(s-c)(s-d)-{\tfrac {1}{4}}(ac+bd+ef)(ac+bd-ef)}}.\end{aligned}}},
where s - semiperimeter

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Area of a general quadrilateral given four sides and two diagonals.Creative Commons Attribution/Share-Alike License 3.0 (Unported)
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Calculate