60-90-120-90 Kite

Calculations at a kite (deltoid) with two right angles, one 60° and one 120° angle. The two right angles and the other two angles are opposite to each other. The 60-90-120-90 kite is a special case of the right kite, it consists of two halved equilateral triangle stichted together at the hypotenuse.
Enter one value and choose the number of decimal places. Then click Calculate.

	Short side (a):
	Long side (b):
	Symmetry diagonal (e):
	Other diagonal (f):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

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

A kite, or deltoid, is a quadrilateral with two adjacent pairs of sides of equal length. Two opposite angles, where the different sides meet, are then equal. This particular kite is a right kite, in which these two opposite angles are right angles. The 60-90-120-90 deltoid can be considered an even more regular form of the right kite, since it can be formed from an equilateral triangle and has the same area as one where the side length is equal to the length of the kite's symmetry diagonal. One of the longer sides of the kite then corresponds to the height of the equilateral triangle, and one of the shorter sides to half of its side length. If the equilateral triangle is divided at the height, two right triangles are formed, which, when joined at the hypotenuse, create the 60-90-120-90 deltoid.
This shape is a very special case of a quadrilateral, which makes a good example of how shapes can be transformed into other, unexpected shapes through decomposition and recomposition. Like for example at the Tangram puzzle, although it doesn't appear in the classic version there.

The 60-90-120-90 deltoid is axially symmetric about its symmetry diagonal, which passes through the two non-right angles. It has no other symmetries.

The kites in the Catalan solids deltoidal icositetrahedron and deltoidal hexacontahedron have different dimensions.

Last updated on 04/23/2026. Author: Jürgen Kummer

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