Kite ABCD: \(AC = e\), \(BD = f\), \(AO = g\) (with \(g < e\))
Kite ABCD: \(AC = e\), \(BD = f\), \(AO = g\) (with \(g < e\))
Given diagonal \(AC = e\), diagonal \(BD = f\) and the distance \(AO = g\) (from top vertex A to the crossing point O on BD), this tool computes all sides, perimeter, area and interior angles.
\[ \begin{aligned} \text{Area} &= \tfrac{1}{2} f e\\\\ a &= \sqrt{\left(\tfrac{f}{2}\right)^2 + (e-g)^2}\\\\ d &= \sqrt{\left(\tfrac{f}{2}\right)^2 + g^2}\\\\ \text{Perimeter} &= 2a + 2d\\\\ \alpha &= 2\arctan\!\left(\tfrac{f}{2g}\right) \times \tfrac{180}{\pi}\\\\ \gamma &= 2\arctan\!\left(\tfrac{f}{2(e-g)}\right) \times \tfrac{180}{\pi}\\\\ \beta &= 180^\circ - \tfrac{\alpha}{2} - \tfrac{\gamma}{2}\\ \end{aligned} \]
Angles: \(\alpha\) at vertex B, \(\beta\) at vertices C and A, \(\gamma\) at vertex D. Sides: \(a = AB = BC\), \(d = AD = DC\).