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Acute-Branch Rhombus Area, Diagonals and Height

Calculate acute-branch rhombus area, diagonals and height with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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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.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Worked inputs Shorter diagonal (f) = 6, Longer diagonal (e) = 8 give Side (a) = 5, Height (h) = 4.8, Area = 24, Perimeter = 20, Angle α = 73.739795, Angle β = 106.2602. Values use the initial displayed units.

A = ef/2 = ah; P = 4a; 4a² = e²+f²

Worked example

Enter these known values and leave the other values blank.

Shorter diagonal (f)
6 cm
Longer diagonal (e)
8 cm
Side (a)
5 cm
Height (h)
4.8 cm
Angle α
73.74 deg
Angle β
106.26 deg
Area
24 cm²
Perimeter
20 cm

Assumptions and limitations

  • The diagonals bisect each other at right angles. This retained workflow requires the shorter diagonal to be strictly shorter, so it uses an acute angle α and excludes the square boundary.
  • Lengths and areas are converted before calculation. Clear an unknown measurement instead of supplying conflicting dimensions.
  • Arithmetic uses 64 significant digits and full-precision π. Display rounding and measurement uncertainty are separate from the underlying arithmetic.

Common questions

Which measurements and inverse branch does this model use?

The diagonals bisect each other at right angles. This retained workflow requires the shorter diagonal to be strictly shorter, so it uses an acute angle α and excludes the square boundary.

Does this acute-branch workflow include a square?

The retained constraints exclude equal diagonals and a 90° acute-angle boundary. Use the square workflow for that equal-diagonal case.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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