Triangular Prism Calculator

A triangular prism is a three-dimensional polyhedron with two parallel congruent triangular bases connected by three rectangular lateral faces. It belongs to the family of prisms, which are characterised by uniform cross-sections along their length. The triangular prism is one of the most commonly encountered 3-D shapes in architecture, engineering, optics, and everyday objects such as tents, wedges, and roof sections. This calculator focuses on right triangular prisms, where the lateral faces are perpendicular to the triangular bases. The key inputs are the three side lengths of the triangular base (a, b, c) and the height of the prism h — the perpendicular distance between the two bases. From these four measurements, the calculator derives four important geometric properties. The base area is calculated using Heron's formula, which requires only the three side lengths. First the semi-perimeter is computed: s = (a + b + c) / 2. Then the area is A_base = √(s(s−a)(s−b)(s−c)). This elegant formula, named after the ancient Greek mathematician Hero of Alexandria, works for any triangle regardless of its type. The volume of the prism is simply the base area multiplied by the height: V = A_base × h. This follows from the general principle that the volume of any prism equals the area of its cross-section times its length. For a right prism, the height h is perpendicular to the bases, so no adjustment is needed. The lateral surface area is the combined area of the three rectangular side faces. Each rectangle has one dimension equal to the corresponding side of the triangle and the other equal to the prism height. The total lateral area therefore equals the perimeter of the triangular base multiplied by the height: A_lateral = (a + b + c) × h. The total surface area adds the lateral area to the areas of both triangular bases: A_total = A_lateral + 2 × A_base. This is the measurement you need when covering or painting the entire outer surface of the prism. Triangular prisms appear across many fields. In optics, glass prisms refract and disperse light into spectra — the principle behind rainbows and spectroscopy. In architecture, triangular prism shapes appear in gabled roofs, dormer windows, and modern glass facades. In civil and structural engineering, triangular prisms form the cross-section of many beams and trusses. In product design, the Toblerone chocolate box is a well-known everyday example. Understanding the volume and surface area of a triangular prism is essential for calculating material quantities, container capacities, and structural weights.