Free · Mathematical relations and geometry

Parallelogram Perimeter from Three Data Sets

Find a parallelogram’s perimeter from adjacent sides, a side with diagonals, or base, height and angle.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Adjacent sides 3 and 4 give perimeter 14. For a rectangle with those sides both diagonals are 5.

P=2(a+b); b²=(e²+f²)/2−a²; b=h/sin θ

Worked example

Enter these known values and leave the other values blank.

Given...
0
Side a
3 cm
Side b
4 cm
Perimeter
14 cm

Assumptions and limitations

  • Opposite sides are equal and parallel. Measurements describe a nondegenerate parallelogram.
  • A side with two diagonals must satisfy the half-diagonal triangle inequalities.
  • The height is perpendicular to the known base; the angle is an interior angle strictly between zero and 180 degrees.
  • Angle inverses use the principal acute branch; its supplementary obtuse angle has the same sine and perimeter.

Common questions

How can I solve for a missing quantity?

Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.

How should I interpret the worked example?

It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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