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Right Trapezoid Area, Slant and Base Inverse Branch

Calculate right trapezoid area, slant and base inverse branch with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
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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 a (base) = 5, b (base) = 8, h (height) = 4 give Area = 26, d (slant side) = 5, δ = 53.130102, γ = 126.8699. Values use the initial displayed units.

A = (a+b)h/2; d² = (b−a)²+h²; γ+δ = 180°

Worked example

Enter these known values and leave the other values blank.

Parallel base (a)
5 cm
Parallel base (b)
8 cm
h (height)
4 cm
Area
26 cm²
Supplementary slant angle (γ)
126.87 deg
Slant angle (δ)
53.13 deg
d (slant side)
5 cm

Assumptions and limitations

  • The parallel bases meet a perpendicular leg of height h. When inferred from slant and height, an unknown base takes the larger-base branch. Inferred δ uses principal arcsine; angle values alone do not choose which base is longer.
  • 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 parallel bases meet a perpendicular leg of height h. When inferred from slant and height, an unknown base takes the larger-base branch. Inferred δ uses principal arcsine; angle values alone do not choose which base is longer.

Does slant length determine which base is longer?

No. Slant and height give the absolute difference between bases. The retained inverse adds that difference to a known base and returns the larger-base branch.

References

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

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