Right Kite Calculator

Name: Right Kite - Geometry Calculator
Author: Jürgen Kummer

Calculations at a right kite or right deltoid. A right kite has two opposite right angles, each between the short and the long sides. The other two angles are an acute angle and an obtuse angle. The kite is a right kite if it has a circumcircle, and vice versa it has a curcumcircle, if it is a right kite. So one of these statements implies the other. A right kite is a special case of a cyclic quadrilateral. Because of the two opposite right angles, the calculation of this shape is much easier than that of a general kite or cyclic quadrilateral. Every deltoid is additionally also a tangent quadrilateral, so it also has an incircle.
Enter the two different side lengths and choose the number of decimal places. Then click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units.

Formulas:

e = \sqrt{a^{2} + b^{2}}

f = \frac{2 a b}{e}

r_{c} = \frac{e}{2}

r_{i} = \frac{a b}{a + b}

p = 2 (a + b)

A = a \cdot b

α = 2 \cdot \arccos (\frac{a^{2} + e^{2} - b^{2}}{2 a e})

γ = 180 ° - α

β = 90 °

Lengths, diagonals, radiuses and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The right kite has exactly one axis of symmetry, which bisects the two opposite angles that are not right angles. This axis divides the quadrilateral into two right triangles, which are mirror-symmetrical to each other. Otherwise this kite has no further symmetries. A right deltoid is formed when one of the two diagonals of a square is moved lengthwise to the left or right, lengthened or shortened, so that both diagonals still intersect and then the adjacent diagonal ends are reconnected.

↑ up