Half square kite calculator and formula
Calculator and formulas for calculating the properties of a half square kite
This calculator calculates area, perimeter, angle and more properties of a half-square kite. The half square kite has a right angle at one of the non-symmetrical corners.
Enter the lengths of sides a and b. Then click on the 'Calculate' button.
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Description
A kite is a quadrilateral that has two pairs of adjacent sides of equal length. The half-square deltoid is a kite quadrilateral that has a right angle at one of the non-symmetrical corners. It also has the following properties:
- The diagonals e and f are perpendicular to each other.
- The diagonal e (from A to C) is the axis of symmetry.
- The diagonal f (from B to D) divides the kite into two isosceles triangles.
- The opposite angles in the corner points B and D are the same size.
Formulas
Side length (a)
\(\displaystyle a= \frac{A}{b · sin(β)}\) \(\displaystyle = \sqrt{ (2· A)- (e_2 · f)}\)
Side length b
\(\displaystyle b= \frac{A}{a · sin(β)}\)
Area (A)
\(\displaystyle A= \frac{a^2+(e2 · f)} {2}\)
Perimater (P)
\(\displaystyle P=2 · (a+b)\)
Diagonal (e)
\(\displaystyle e= \sqrt{a^2 + b^2 - (2 · a · b · cos(β))}\)
Diagonal (f)
\(\displaystyle f= \sqrt{2} · a)\)
Angle (γ)
\(\displaystyle γ = arccos \left(\frac{2 * b^2 - f^2}{2 * b^2}\right)\)
Angle (β)
\(\displaystyle β = (270 - γ) / 2 \)
Section (e1)
\(\displaystyle e_1 = \frac{a}{\sqrt{2}}e\)
Square • Rectangle • Golden Rectangle • Rectangle to Square • Rhombus, given varios parameter • Rhombus , given diagonal e, f • Parallelogram, given 2 sides and angle • Parallelogram area, given side and height • Trapezoid • Cyclic Quadrilateral • General Quadrilateral • Concave Quadrilateral • Arrowhead Quadrilateral • Crossed Square • Frame • Kite, given 2 diagonal and distance • Kite Area, given 2 diagonal • Half Square Kite • Right Kite"
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