Triangular Prism Calculator
A triangular prism is the solid you get by taking a triangle and extending it straight back to a given length. You see it everywhere: a Toblerone bar, a tent, a roof truss, a wedge door stop, and a glass prism that splits light are all triangular prisms. This calculator takes the three sides of the triangular cross-section and the length of the prism and returns the volume, total surface area, and triangle area in one step. The volume follows the rule that applies to every prism: find the area of the cross-section and multiply by the length. The clever part is the cross-section, because providing three side lengths is the most flexible way to describe a triangle, and the calculator finds its area using Heron's formula, which needs nothing more than those three sides. The surface area adds the two triangular end faces to the three rectangular side faces, which together come to twice the triangle area plus the triangle's perimeter times the prism length. You do not need to measure the height of the triangle separately. Enter the three sides of the base triangle and the prism length in any consistent unit, and the calculator updates instantly. It also checks whether the three sides form a valid triangle and flags the result if they do not. Use this tool for geometry homework, calculating the capacity of a trough or hopper, working out material for a ridge section in construction, or any problem involving a triangular cross-section solid.
The three sides must form a valid triangle (each side less than the sum of the other two).
How it works
The triangle area uses Heron's formula: with semi-perimeter s = (a + b + c) / 2, area = √(s(s-a)(s-b)(s-c)). Volume = triangle area × prism length. Surface area = 2 × triangle area + (a + b + c) × length, which adds the two triangular end faces to the three rectangular side faces.
Worked example
For a 3-4-5 right triangle with prism length 10: semi-perimeter s = (3 + 4 + 5) / 2 = 6. Triangle area = √(6 × 3 × 2 × 1) = √36 = 6 square units. Volume = 6 × 10 = 60 cubic units. Surface area = 2 × 6 + (3 + 4 + 5) × 10 = 12 + 120 = 132 square units. These match the pre-filled defaults above.
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