Calculate volume and surface area of a triangular prism. Supports equilateral, right, and scalene base triangles with prism length input.
The Volume of a Triangular Prism Calculator computes the volume, lateral surface area, and total surface area for a prism with a triangular cross-section. A triangular prism is a three-dimensional shape with two congruent triangular faces (bases) connected by three rectangular faces. These shapes are common in architecture (roof ridges, A-frame cabins), engineering (structural beams, trusses), packaging (Toblerone boxes), and optics (glass prisms). The volume equals the base triangle area multiplied by the prism length: V = A_base × L. This calculator supports three base-triangle modes. In Equilateral mode, enter the side length and the calculator derives the area using A = (√3/4)s². In Right Triangle mode, enter the two legs and the hypotenuse is computed. In Scalene mode, enter all three sides and Heron's formula determines the area. Each mode also computes the perimeter of the base, the lateral surface area (perimeter × length), and the total surface area (lateral area + 2 × base area). Eight preset configurations cover common prism sizes from small optic prisms to large structural beams. A formulas reference table shows every equation at a glance, and visual bars display dimension proportions to help you verify your inputs.
Triangular prisms appear in roof sections, beams, packaging, and optical components, but the calculation path changes depending on the triangle that forms the base. This calculator keeps the geometry organized across equilateral, right, and scalene cases so you can move from side lengths to base area, then to prism volume and surface area, without having to switch formulas manually.
Volume V = A_base × L. Equilateral base area A = (√3/4)s². Right triangle area A = ½·a·b. Scalene area via Heron: A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2. Lateral area = perimeter × L. Total SA = lateral area + 2·A_base.
Result: Base area ≈ 15.5885, volume ≈ 155.8846, total surface area ≈ 211.1769
Equilateral base with side 6, length 10: A = (√3/4)·36 ≈ 15.59. V = 15.59 × 10 = 155.88. Perimeter = 18. Lateral area = 18 × 10 = 180. Total SA = 180 + 2·15.59 = 211.18.
The defining step in any triangular prism problem is finding the area of the triangular base. For an equilateral triangle, symmetry gives a compact formula. For a right triangle, the two legs make the area immediate. For a scalene triangle, you usually need Heron's formula because no altitude is given directly. Once the base area is known, the prism volume is just that area extended through the prism length.
Students often confuse volume and surface area because both depend on the same base triangle. The volume multiplies base area by prism length, but the lateral surface area uses the base perimeter instead. Each side of the triangle creates one rectangular face, so the total side area is perimeter times length. This calculator shows that breakdown explicitly in the rectangular-face table.
Triangular prisms are practical models for roof trusses, tent profiles, wedges, and packaging with triangular cross-sections. In those settings, the base mode matters: a roof cross-section may be isosceles or scalene, while an engineered prism may use a right-triangle section. Choosing the correct base model first prevents bad volume estimates later, especially when material quantities or surface coverings depend on the result.
A triangular prism is a 3D shape with two parallel, congruent triangular faces connected by three rectangular lateral faces. Use this as a practical reminder before finalizing the result.
Volume = base triangle area × prism length. Calculate the triangle area first, then multiply by the length.
The lateral surface area is the sum of the three rectangular side faces: base perimeter × prism length. Keep this note short and outcome-focused for reuse.
Heron's formula computes the area of a triangle from its three sides: A = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.
Yes — select Scalene mode and enter any three valid side lengths. The calculator also supports equilateral and right triangle shortcuts.
Roof ridges, A-frame buildings, Toblerone packaging, optical prisms, camping tents, bridge trusses, and structural beams. Apply this check where your workflow is most sensitive.