Kite Area Calculator
This kite area calculator works for the geometric quadrilateral: enter the diagonals with a segment, two sides with the symmetry axis, or two sides with the angle between them. Example: e = 10, f = 6 and p = 4 give sides 5 and 6.71, area 30 and perimeter 23.42.
Source: Wikipedia – Drachenviereck. Updated: .
How it is calculated
A kite has two pairs of equal adjacent sides and a symmetry axis that is also a diagonal. The diagonals meet at right angles, and the axis bisects the cross diagonal. With three suitable inputs the calculator finds everything else.
Names and formulas
The vertices are A, B, C, D with sides AB = AD = a and CB = CD = b. The symmetry axis is e = AC, the cross diagonal is f = BD, and M is their intersection with segments p = AM and q = MC. The area is A = e·f / 2 and the perimeter P = 2·(a + b). From the diagonals and segment the sides follow by the Pythagorean theorem: a = √(p² + (f/2)²) and b = √(q² + (f/2)²). If two sides and the axis are known, the law of cosines in triangle ABC gives the height onto the axis and with it f.
Example
For e = 10, f = 6 and p = 4 we get q = 6, a = √(16 + 9) = 5 and b = √(36 + 9) ≈ 6.71. The area is 30 and the perimeter 2·(5 + 6.71) ≈ 23.42. The angles are 73.74° at A, 53.13° at C and 116.57° each at B and D.
- The angles of a quadrilateral add up to 360°; the angles at B and D are equal.
- If a = b the kite is a rhombus; if all angles are also 90° it is a square.
- For “two sides and angle” the angle between a and b at B is meant.
Frequently asked questions
How do you calculate the area of a kite?
From the diagonals: A = e·f / 2, where e is the symmetry axis and f the cross diagonal. You can also add the two triangles ABC and ADC.
How do you calculate the perimeter of a kite?
P = 2·(a + b), twice the sum of the two different side lengths.
How does a kite differ from a rhombus?
In a kite only adjacent sides are equal in pairs. In a rhombus all four sides are equal, so a rhombus is a special kite.
Sources and legal basis
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