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Area of a Quadrilateral (from 4 Sides and the Sum of Opposite Angles)

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Calculate the area and perimeter of a quadrilateral using its four side lengths and the sum of one pair of opposite angles.
Side a
Side b
Side c
Side d
Sum of opposite angles: θ1 + θ2
Area S 
Perimeter L 
\(\normalsize Bretschneider's\ formula \\ (1)\ area:\ S=\sqrt{(s{\small-}a)(s{\small-}b)(s{\small-}c)(s{\small-}d){\small-}abcd\cos^{\small2}\frac{\theta}{2}}\\ \hspace{100px} s={\large\frac{a+b+c+d}{2}}\ ,\hspace{10px} \theta=\theta_1+\theta_2\\(2)\ perimeter:\ L=2s=a+b+c+d\)

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