Calculations at an X-shape. This is formed, when a parallelogram shaped bar is reflected and connected with the original bar in the center. The intersection of both bars is a rhombus with the side length x.
Enter length and thickness of one bar and one angle. Choose the number of decimal places and click Calculate. Please enter angles in degrees, here you can convert angle units.
Formulas:
α + β = 180°
γ = 90° - α/2
x = b * sin( γ ) / sin( 2γ )
m = l / 2
n = m - x
h = 2m * sin( β/2 )
i = 2n * sin( α/2 ) + 2b
p = 4 * ( b + m + n )
A = 2 * l * b * sin( α ) - x² * sin( α )
Lengths, thickness, heights and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
An X is sometimes also called a cross, but here these two terms here refer to different shapes. This X is based on parallelograms, whereas the cross is based on rectangles. The two shapes cannot be reconciled either, because in the X-shape the lower and upper end sides are parallel, whereas in the cross the adjacent end sides are perpendicular to each other.
The X-shape is point-symmetrical to its center and axially symmetrical to each of the two bisectors through two opposite, inner corners. It is rotationally symmetrical at an angle of 180 degrees and multiples thereof.
The X is shown in many sans serif fonts in the form shown here. St. Andrew's crosses sometimes have this shape, but most of the time the upper and lower end sides are not shown parallel. If the St. Andrew's cross has a frame that cuts off the cross at the top and bottom, but not at the left and right, then such an X-shape is created.
X-shapes of various types, including the one shown here, are often found on half-timbered houses. They are often used in coats of arms and national emblems, where they usually have a Christian reference and can be traced back to the St. Andrew's Cross.