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Parallelogon Calculator

Calculations at 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.

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)




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