Kite Calculator

Name: Kite - Geometry Calculator
Author: Jürgen Kummer

Calculations at a kite or a deltoid. A kite is a quadrilateral with two neighboring pairs of sides with equal length, respectively a quadrilateral whose one diagonal lies on the symmetry axis. The two diagonals are perpendicular to each other.
Enter either the lengths of both diagonals or of both sides, as well as the distance of the points A and E. Choose the number of decimal places and click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units.

Formulas:

a = \sqrt{{(\frac{f}{2})}^{2} + c^{2}}

b = \sqrt{{(\frac{f}{2})}^{2} + {(e - c)}^{2}}

f = 2 \sqrt{a^{2} - c^{2}}

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

p = 2 \cdot (a + b)

A = \frac{e f}{2}

r_{i} = \frac{2 A}{p}

α = \arccos (\frac{c^{2} + a^{2} - {(\frac{f}{2})}^{2}}{2 \cdot c \cdot a})

γ = \arccos (\frac{{(e - c)}^{2} + b^{2} - {(\frac{f}{2})}^{2}}{2 \cdot (e - c) \cdot b})

β = \frac{360 ° - α - γ}{2}

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

The kite is axially symmetric to the symmetry diagonal between the two non-equal angles. When the half kite has a right angle opposite to the dividing symmetry axis, only then it has an circumcircle. Its center is in the middle of the symmetry axis.

perimeter p, area A

sides and angles

diagonals

bisecting lines and incircle

circumcircle

A special form of the kite with four sides of equal length is the rhombus. Other special kites or deltoids are the 60-90-120-90 deltoid, the half square kite and the right kite. The arrowhead quadrilateral, which other than the deltoids mentioned before is non-convex, is sometimes counted as a kite. Kites form the side surfaces of the two Catalan bodies deltoidal icositetrahedron and deltoidal hexecontahedron. The name of the kite comes from the kite play device, which is carried upwards by the wind hanging on a string and stands or can be moved in the air. These kites are often deltoid shaped and were originally made of fabric attached to a wooden cross. The name Deltoid refers to the large ancient Greek letter Delta Δ, which has the shape of a isosceles triangle. The deltoid consists of two isosceles triangles attached to each other.

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