Calculations in a unicursal hexagram. This is made of two long and four short diagonals of a hexagon. Other than a regular hexagram, this can be drawn in one go, without lifting the pen. The short diagonal b is split into three pieces of different length, the long diagonal c is split into four pieces of equal length. Both large spikes have an angle of 60°, the four small spikes are rectangular to the large ones. The area is calculated as that of a rhombus with the side length b1+b2 plus the equal right triangles of the four small spikes. Enter one value and choose the number of decimal places. Then click Calculate.
b = √3 * a
b1 = b/2 = √3 / 2 * a
b2 = b/6 = √3 / 6 * a
b3 = b/3 = √3 / 3 * a
c = 2 * a
c' = c/4 = a/2
p = 4b1 + 4b3 + 4c' = ( 2 + 10/3 * √3 ) * a
A = ( b1 + b2 )² * sin(60°) + 2b2c' = 5/6 * √3 * a²
Edge length, diagonals, sections and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).