Star of Lakshmi calculator and formula

This function calculates various parameters of a Star of Lakshmi.

To perform the calculation, select the property you know from the pull down menu and enter its value. Then click the 'Calculate' button.

Star of Lakshmi calculator

Input

Decimal places

Results

Square edge a

Octagon edge b

Star edge c

Chord length l

Perimeter P

Octagon area Ao

Star area As

Formulas for the Star of Lakshmi

Edge length of the square

\(\displaystyle a=2 · c+b\)

Edge length of the octagon

\(\displaystyle b= (\sqrt{2}-1) ·a\)

Edge length of the star

\(\displaystyle c= \frac{(2 - \sqrt{2}) · a}{2}\)

Chord length

\(\displaystyle l = 2 ·c · cos\left(\frac{π}{8}\right)\)

Perimeter

\(\displaystyle P = 16 · c\)

Area of the octagon

\(\displaystyle Ao = 2 · (\sqrt{2} - 1) · a^2\)

Area of the star

\(\displaystyle As = 2 · (2 - \sqrt{2}) · a^2\)

Star of Lakshmi calculator

Calculate the Star of Lakshmi

Formulas for the Star of Lakshmi

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