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Home | Forms | Contact & Privacy Geometric Calculators German: Geometrierechner

2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, Hexadecagon, N-gon

Other Polygons:
Triangle, Right Triangle, Isosceles Triangle, IR Triangle, Quadrilateral, Rectangle, Rhombus, Parallelogram, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Concave Pentagon, Parallelogon, Threestar, Fourstar, Pentagram, Hexagram, Oktagram, Star of Lakshmi, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Ellipse, Elliptical Segment, Stadium, Digon, Spherical Triangle, Spiral, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Arbelos, Salinon, Lune, Oval, Three Circles, Lemniscate, Squircle
3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

Archimedean Solids:
Truncated Tetrahedron, Cuboctahedron, Truncated Cube, Truncated Octahedron, Rhombicuboctahedron, Icosidodecahedron, Truncated Dodecahedron, Truncated Icosahedron

Catalan Solids:
Triakis Tetrahedron, Rhombic Dodecahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Rhombic Triacontahedron

Johnson Solids:
Pyramids, Cupolae, Rotunda, Elongated Pyramids, Snub Disphenoid

Other Polyhedrons:
Cuboid, Square Pillar, Square Pyramid, Regular Pyramid, Pyramid, Regular Frustum, Frustum, Bipyramid, Ramp, Right Wedge, Wedge, Rhombohedron, Parallelepiped, Prism, Oblique Prism, Antiprism, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Half Cuboid, Skewed Cuboid, Truncated Rhombohedron, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron

Round Forms:
Sphere, Hemisphere, Cylinder, Cut Cylinder, Oblique Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Spheroid, Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Spherical Shell, Cylindrical Shell, Spherical Ring, Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


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Parallelogon Calculator

Calculations in a convex, hexagonal parallelogon or elongated parallelogram. A parallelogon is a polygon with parallel opposite sides of equal length each, which can be used to tile a plane without gap, so that the edges fit together. There are only four- and six-sided parallelogons. A four-sided parallelogon is called parallelogram. Enter the three side lengths and two of the angles. The angles must be smaller than 180°. Choose the number of decimal places and click Calculate. Please enter angles in degrees, here you can convert angle units.


Euclid Side a: Parallelogon
Parallelogon with caption
Parallelogon with the diagonals da, db and dc (red), as well as dab, dac and dbc (blue).
Side b:
Side c:
Angle α:
Angle β:
Angle γ:
Short diagonal da:
Short diagonal db:
Short diagonal dc:
Long diagonal dab:
Long diagonal dac:
Long diagonal dbc:
Height ha:
Height hb:
Height hc:
Perimeter (p):
Area (A):
Round to    decimal places.



Formulas:
α + β + γ = 360°

da = √b² + c² - 2bc * cos( α )
db = √a² + c² - 2ac * cos( β )
dc = √a² + b² - 2ab * cos( γ )

dab = √a² + da² - 2ada * cos{ arccos[ ( a² + dc² - b² ) / 2adc ] + arccos[ ( da² + dc² - db² ) / 2dadc ] }
dac = √a² + da² - 2ada * cos{ arccos[ ( a² + db² - c² ) / 2adb ] + arccos[ ( da² + db² - dc² ) / 2dadb ] }
dbc = √b² + db² - 2bdb * cos{ arccos[ ( b² + da² - c² ) / 2bda ] + arccos[ ( db² + da² - dc² ) / 2dbda ] }

ha = da * sin{ arccos[ ( a² + da² - dac² ) / 2ada ] }
hb = db * sin{ arccos[ ( b² + db² - dab² ) / 2bdb ] }
hc = da * sin{ arccos[ ( c² + dc² - dbc² ) / 2cdc ] }

p = 2 * ( a + b + c )

v = a + b + dc
w = a + db + c
x = da + b + c
y = da + db + dc
A = v/2 * (v/2-a) * (v/2-b) * (v/2-dc) + w/2 * (w/2-a) * (w/2-db) * (w/2-c) + x/2 * (x/2-da) * (x/2-b) * (x/2-c) + y/2 * (y/2-da) * (y/2-db) * (y/2-dc)

Lengths, diagonals, heights and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).




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