Calculator and formula for kite quadrilateral area, angle and perimeter
This function calculates the properties of a kite. A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
For the calculation, enter the lengths of the two diagonals an e and f and the distance c. In result the angles are displayed in degrees.
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The diagonals e and f are perpendicular to each other.
The diagonal \(\displaystyle AC = e \) is the axis of symmetry.
The diagonal \(\displaystyle BD = f \) divides the kite square into two isosceles triangles.
The opposite angles in the corner points \(\displaystyle B \) and \(\displaystyle D \) are equal.
\(\displaystyle a= \sqrt{ \left(\frac{f}{2}\right)^2 + c^2}\)
\(\displaystyle b= \sqrt{ \left(\frac{f}{2}\right)^2 + (e-c)^2}\)
\(\displaystyle A=\frac{e · f}{2}\)
\(\displaystyle A=a · b · sin(β)\)
\(\displaystyle P=2 · a + 2 · b\)
\(\displaystyle P=2 · (a+b)\)
\(\displaystyle e= \sqrt{a^2+b^2-2 · a · b ·cos(β)}\)
\(\displaystyle f= 2 · a · sin\left(\frac{α}{2}\right)\)
\(\displaystyle f= 2 · b · sin\left(\frac{γ}{2}\right)\)
\(\displaystyle α = arccos\left(\frac{2 · a^2 - f^2}{2 · a^2} \right)\)
\(\displaystyle γ = arccos\left(\frac{2 · b^2 - f^2}{2 · b^2} \right)\)
\(\displaystyle β = δ = arccos\left(\frac{a^2+ b^2 - e^2}{2 · a · b} \right)\)
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