Calculations at a parallelogram. A parallelogram or rhomboid is a convex quadrilateral with parallel opposite sides of the same length and opposite angles of the same size.
Enter the two side lengths and one angle and choose the number of decimal places. Then click Calculate. Please enter angles in degrees, here you can convert angle units.
Formulas:
β = 180° - α
e = √ a² + b² - 2 * a * b * cos ( β )
f = √ a² + b² - 2 * a * b * cos ( α )
p = 2 * ( a + b )
A = a * b * sin ( α ) = a * ha = b * hb
ha = b * sin ( α )
hb = a * sin ( α )
Side lengths, diagonal, perimeter and heights have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
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The centroid is at the intersection of the diagonals. To this, the parallelogram is point symmetric and rotationally symmetric at a rotation of 180° or multiples of this. By cutting off one corner and adding this piece on the other side, the parallelogram can be turned into a rectangle.
perimeter p, area A
sides and angles
diagonals
heights
turning the parallelogram into a rectangle
The parallelogram can be thought of as a distorted rectangle, of which it is a more general form. Like the rectangle, the square and the rhombus are also special forms of the parallelogram. The parallelogram, in turn, is a special form of the trapezoid. The crossed counterpart to the parallelogram is the antiparallelogram. The three-dimensional equivalent of the parallelogram is a parallelepiped.
Parallelograms are point-symmetrical to their center and rotationally symmetrical with the number 2, i.e. with a rotation of 180 degrees. Using parallelograms, the plane can be tiled without any gaps. Each of the two diagonals splits the parallelogram into two congruent triangles that are shifted 180 degrees from each other.
