Calculations at a cross. Here a cross are two equal rectangles, which intersect perpendicularly in their centers. So each of the four arms of the cross has the same length and the same width. The arm length is measured from one corner at the end of the arm to the nearest inner angle. The result is a rectangular, concave dodecagon with 8 inner and 4 outer right angles.
Enter two of the three values a, b and l, choose the number of decimal places and click Calculate.
Formulas:
l = 2a + b
rc = √ (l/2)² + (b/2)²
p = 8a + 4b
A = 4ab + b²
Lengths, width, radius and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The geometric shape of such a cross has a smaller surface area and circumference than the two rectangles placed on top of each other that make it up. This is because the intersection, which has the shape of a square with side length b, only occurs once in the cross, but twice in the two rectangles. The surface area of the cross is therefore b² smaller, and the perimeter is 4b smaller, as the middle square is completely absent here.
The cross is of course particularly known as a Christian symbol, although it is usually represented here with a long lower bar, medium-length and equal bars on the left and right, and a short bar on the top. The calculation is then only slightly more complicated and is carried out similar to this cross. The cross with four bars of equal length is also often found as a Christian symbol, here the degree of abstraction is slightly higher.
A cross with four arms of equal length and width is point-symmetrical to the center. It is axially symmetrical to the two axes in the middle through the opposite cross ends and to the two axes through the opposite inner corners. It is rotationally symmetric at an angle of 90 degrees and multiples thereof.