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Surface Area of a Triangular Prism — result sheet
Calculate the total surface area of a straight triangular prism from three valid base sides and prism length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: S=2A_triangle+(a+b+c)L, with A_triangle=sqrt(s(s-a)(s-b)(s-c)), s=(a+b+c)/2, and all strict triangle inequalities required.
A straight triangular prism has two congruent triangular ends and three rectangular lateral faces. Heron's formula finds the base area from the three side lengths, and the triangle perimeter times prism length gives the lateral area.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Triangle side a — length units; First side of the triangular base.; minimum 1.0E-6; maximum 1000000
- Triangle side b — length units; Second side of the triangular base.; minimum 1.0E-6; maximum 1000000
- Triangle side c — length units; Third side of the triangular base.; minimum 1.0E-6; maximum 1000000
- Prism length L — length units; Distance between the two congruent triangular ends.; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Triangle side a | 3 |
| Triangle side b | 4 |
| Triangle side c | 5 |
| Prism length L | 10 |
The 3-4-5 base has area 6 and perimeter 12, so total surface area is 2(6)+12(10)=132 square units.
Assumptions and limits
- The three positive base sides form a nondegenerate triangle satisfying all strict triangle inequalities.
- The prism is straight with two congruent parallel triangular ends and rectangular lateral faces, and prism length uses the same length unit as the base sides.
- The result is ideal total surface area; edge thickness, bevels, openings, material, and construction tolerances are not inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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