Calculations at a sharp kink or folded rectangle. This is a special shape of a concave hexagon. Enter the width, the short or long side of each leg and the angle. The angle must be smaller than 180°. Choose the number of decimal places and click Calculate. Please enter the angle in degrees, here you can convert angle units.
Formulas:
d = b / sin(α/2)
a = c + √ d² - b²
a' = c' + √ d² - b²
a - c = a' - c'
p = a + 2b + c + a' + c'
A = b * ( a + c' )
Lengths, width, diagonal and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
This kink has four right angles, an acute or obtuse angle and a super-obtuse angle. Two of the right angles are at each end, the other two angles are in the middle. The acute or obtuse angle is the decisive one, the bend angle α. The super-obtuse angle results from this as 360°−α.
If the bend angle is 90 degrees, i.e. a right angle, then the kink is an L-shape. The calculation is easier with this and does not require a sine. It is of course even easier with an angle of 180 degrees, because then the shape is a normal rectangle of length a+a' and width b.
Such a kink cannot simply be broken down into rectangles, a right kite remains as an intermediate piece. Therefore, a real rectangular workpiece cannot be bent into this shape without something sticking out, being distorted or breaking off. This may be important to consider if the calculation is not just about a mathematical object, but about a physical one. The best way to create such a kink is to put together two rectangles by removing a right triangle of the same size from one end of each. These two triangles, put together in mirror image at the hypotenuse, correspond to the protruding kite.