Arrowhead Quadrilateral calculator and formulas

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.

Arrowhead calculator

Input

Decimal places

Results

Long side a

Short side b

Length l

Height h

Inner length m

Missing length n

Area A

Perimeter U

Angle α

Angle β

Angle γ

Formulas for the arrowhead quadrilateral

Long side a

\(\displaystyle a =\frac{b·sin\left(\frac{β}{2}\right)}{sin\left(\frac{α}{2}\right)} \)

Short side b

\(\displaystyle b =\frac{a·sin\left(\frac{α}{2}\right)}{sin\left(\frac{β}{2}\right)} \)

Angles

\(\displaystyle α+β+2·γ= 360°\)

Inner length

\(\displaystyle m= \frac{a·sin(γ)} { sin\left(\frac{β}{2}\right) }\)

Missing length

\(\displaystyle n= b·sin\left(\frac{β}{2-90°}\right) \)

Length

\(\displaystyle l= m+n\)

Height

\(\displaystyle h=2·\sqrt{b^2-n^2}\)

Perimeter

\(\displaystyle h=2·\sqrt{b^2-n^2}\)

Area

\(\displaystyle A=\frac{l·h}{2}-\frac{n·h}{2}\)

Arrowhead Quadrilateral

Calculate arrowhead quadrilateral

Formulas for the arrowhead quadrilateral

Quadrilateral Functions

More Geometric Functions