Free · Geometry and function relationships

Special Right Triangle Ratios and Area

Choose a 45–45–90, 30–60–90, fixed-leg-ratio or 3–4–5 triangle. Scale its sides together; perimeter scales linearly and area scales quadratically.

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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.

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

Formula and method

For given = 4, a5 = 3, b5 = 4, c5 = 5, area5 = 6, perimeter5 = 12.

c=√(a²+b²); A=ab/2; P=a+b+c

Worked example

Enter these known values and leave the other values blank.

Special triangle
4
a
3 cm
b
4 cm
c
5 cm
Perimeter
12 cm
Area
6 cm²

Assumptions and limitations

  • Choose a 45–45–90, 30–60–90, fixed-leg-ratio or 3–4–5 triangle. Scale its sides together; perimeter scales linearly and area scales quadratically.
  • Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
  • Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

Choose a 45–45–90, 30–60–90, fixed-leg-ratio or 3–4–5 triangle. Scale its sides together; perimeter scales linearly and area scales quadratically.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

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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