Calculations at a crossed rectangle. This is a rectangle with two adjacent vertices swapped. It consists of two identical isosceles triangles. Enter the two side lengths of the original rectangle. Choose the number of decimal places, then click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units. The length of the leg c is the length of a leg of one of the isosceles triangles.
Formulas:
c = √ a² + b² / 2
γ = arccos( (2c² - a²) / (2c²) )
β = 180° - γ
α = β / 2
p = 2a + 4c
A = ab / 2
Lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The crossed rectangle has two perpendicular axes of symmetry and is point-symmetrical to their intersection point. A crossed rectangle is not a quadrilateral in the usual sense, as it has more than four corners. However, it is often mentioned in connection with quadrilaterals, for example when the different types of quadrilaterals are listed. How the intersection point is counted is unclear and probably a matter of definition. It can be seen as two corners, which would make the crossed rectangle a concave hexagon. However, the two triangles are only connected at one point, which is not normally the case with concave polygons. Crossed polygons are therefore a separate class of polygons with special properties. They are somewhat related to star polygons such as pentagram and hexagram, which can also be considered crossed, but which are not connected at just one point at any place. Another crossed quadrilateral is the antiparallelogram. The crossed rectangle and the antiparallelogram have a regularity; for irregular concave quadrilaterals it is best to calculate with the two individual triangles.