Arrowhead Quadrilateral
Calculator and formulas for a arrowhead quadrilateral
This function calculates various parameters of a arrowhead quadrilateral.
In an arrowhead quadrilateral, one of the two diagonals lies outside the figure. The diagonals are perpendicular to each other at the point of intersection.
To calculate, select the known side length from the menu and enter its value. Choose the two known angles from the menus and enter their values. Then click on the 'Calculate' button.
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Formulas for the arrow square
Side length (a)
\(\displaystyle a =\frac{b·sin\left(\frac{β}{2}\right)}{sin\left(\frac{α}{2}\right)} \)
Side length (b)
\(\displaystyle b =\frac{a·sin\left(\frac{α}{2}\right)}{sin\left(\frac{β}{2}\right)} \)
Angle (α)
\(\displaystyle α+β+2·γ= 360°\)
Inside length (m)
\(\displaystyle m= \frac{a·sin(γ)} { sin\left(\frac{β}{2}\right) }\)
Missing length (n)
\(\displaystyle n= b·sin\left(\frac{β}{2-90°}\right) \)
Length (l)
\(\displaystyle l= m+n\)
Height (h)
\(\displaystyle h=2·\sqrt{b^2-n^2}\)
Perimeter (P)
\(\displaystyle P=2·\sqrt{b^2-n^2}\)
Area (A)
\(\displaystyle A=\frac{l·h}{2}-\frac{n·h}{2}\)
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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