Kite Calculator

Calculate the area, perimeter, and side lengths of a kite from its two diagonals.

Results

Area

30.00

Perimeter

23.32

Side a

5.83

Side Comparison

Kite Calculator

PropertyValue
Area30.0000
Perimeter23.3238
Side a5.8310
Side b5.8310

About the Kite Shape

What Is a Kite?

A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. Unlike a parallelogram, the equal sides are adjacent rather than opposite. The diagonals of a kite always intersect at right angles, with one diagonal bisecting the other.

Area Formula

The area of a kite is calculated as A = (d1 x d2)/2, where d1 and d2 are the lengths of the two diagonals. This formula works because the diagonals are perpendicular, creating four right triangles whose areas sum to the total.

Properties

A kite has one axis of symmetry along the longer diagonal. The diagonals are perpendicular, and the longer diagonal bisects the shorter one. One pair of opposite angles are equal. If all four sides are equal, the kite is also a rhombus.

Applications

Kite shapes appear in actual kites (the flying toy), architectural details, quilting patterns, and geometric constructions. The perpendicular diagonal property makes kites useful in structural design where right-angle bracing is needed.

Practical Example

Kite with d1=10, d2=6

Step 1: Area = (10 x 6)/2 = 30

Step 2: Half-diagonals: 5 and 3

Step 3: Side = sqrt(5² + 3²) = sqrt(34) = 5.83

Step 4: Perimeter = 4 x 5.83 = 23.32

Perguntas Frequentes

Is a rhombus a special type of kite?

Yes. A rhombus is a kite where all four sides are equal. Since a rhombus has two pairs of adjacent equal sides, it satisfies the definition of a kite.

Are the diagonals always perpendicular?

Yes, the diagonals of a kite always intersect at right angles (90 degrees). This is a defining property of kites.

Does a kite have any parallel sides?

Generally, no. A kite does not typically have parallel sides. The only exception is when the kite is also a rhombus (all sides equal), in which case opposite sides are parallel.

How do I find the side lengths?

Using the half-diagonals and Pythagorean theorem: side = sqrt((d1/2)² + (d2/2)²). For a symmetric kite, all four sides have the same length calculated this way.

What is the perimeter formula?

Perimeter = 2a + 2b, where a and b are the two different side lengths. If both pairs of adjacent sides are equal to the same value, P = 4s.

Disclaimer: This calculator uses standard geometric formulas. Results are for informational purposes only.

References

  1. Wikipedia. "Regular polygon." en.wikipedia.org
  2. Wolfram MathWorld. mathworld.wolfram.com

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