Free · Algebra and geometric models

Triangular Prism Volume and Surface Measures

Calculate prism volume and surface area from six descriptions of its triangular cross-section.

  • 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

For the worked inputs, Prism volume = 60, Prism surface area = 132.

V=Bℓ; total area=2B+ℓ(a+b+c)

Worked example

Enter these known values and leave the other values blank.

Triangle type
0
Side length a
3 cm
Side length b
4 cm
Prism length (L)
10 cm
Side length c
5 cm
Prism volume
60 cm³
Prism surface area
132 cm²

Assumptions and limitations

  • The prism is right: length is perpendicular to parallel triangular faces.
  • The base-only mode does not determine surface area unless all three side lengths are known. ASA angles are positive and sum to less than 180 degrees.
  • The tablespoon and teaspoon choices mean metric 15 mL and 5 mL volumes. Cups use US customary volume.

Common questions

What must I enter?

Choose the mode when available and enter its independent known quantities. Leave an unknown editable quantity empty to use a supported inverse.

How should I use the result?

Interpret the numbers within the stated mathematical assumptions. Available unit selectors convert quantities; display rounding does not replace the internal calculation.

References

The captured ASA volume inverse fabricated a constant π angle. Cotangent addition with volume/length recovers a valid interior angle, including obtuse cases. Explicit real-model bounds validate dimensions, inverse branches and discrete controls omitted or approximated in this capture. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume.

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