Calculate the total and lateral surface area, volume, and face-by-face breakdown of a triangular prism. Supports isosceles, equilateral, and scalene triangle cross-sections.
A triangular prism is a three-dimensional solid with two congruent triangular faces (the ends) and three rectangular faces (the sides). It is one of the most common prism shapes, found in everyday objects like tents, Toblerone chocolate boxes, roof structures, cheese wedges, and architectural features.
The total surface area of a triangular prism is the sum of the areas of its five faces: two triangular ends and three rectangular sides. The lateral surface area includes only the three rectangular faces — the part you would wrap with material if the ends were left open. The volume is simply the area of the triangular cross-section multiplied by the prism length.
Calculating these values requires knowing the triangular cross-section dimensions and the prism length. This calculator supports three input modes: (1) base + height for isosceles or right triangles, (2) three sides for any scalene triangle (using Heron's formula), and (3) a single side for equilateral triangles. Each mode computes all three triangle sides, which determine the three rectangular face dimensions.
Practical applications are widespread. Architects use triangular prism geometry for roof trusses. Packaging engineers need the surface area to estimate material for triangular boxes. Tent manufacturers calculate fabric area for tent walls and ends. HVAC engineers use it for triangular duct sizing. This calculator provides a full breakdown with visual bars showing each face's percentage contribution, making it easy to identify which surfaces dominate the total area.
Triangular prisms often require a two-step calculation: first find the triangle's area and perimeter, then use those results to build the prism's lateral area and total surface area. That makes them more error-prone than rectangular prisms, especially when the cross-section is scalene and Heron's formula is involved. This calculator keeps those dependencies connected so one set of inputs updates every face area automatically.
It is especially useful for tents, roof sections, triangular cartons, and wedge-shaped enclosures where you need both total material coverage and the side-only area. The face-by-face table makes it easy to check which rectangular panel is largest and whether the triangular ends are a major or minor part of the total.
Triangle area (base × height): A = ½ × b × h Triangle area (Heron's): A = √[s(s−a)(s−b)(s−c)], s = (a+b+c)/2 Equilateral triangle: A = (√3/4) × a² Two triangular ends = 2 × A Rectangular face = side × prism length Lateral SA = (s₁ + s₂ + s₃) × L = perimeter × L Total SA = 2A + perimeter × L Volume = A × L
Result: Total SA = 184 cm², Lateral SA = 160 cm², Volume = 120 cm³
In Base + Height mode, enter sideA = 6 cm, sideB = 4 cm, and prismLength = 10 cm. The triangular cross-section area is ½ × 6 × 4 = 12 cm². Because the calculator assumes an isosceles triangle in this mode, each slanted side is √((6/2)² + 4²) = √25 = 5 cm, so the triangle perimeter is 6 + 5 + 5 = 16 cm. Lateral surface area is perimeter × prism length = 16 × 10 = 160 cm², total surface area is 160 + 2(12) = 184 cm², and volume is 12 × 10 = 120 cm³.
For any prism, volume comes from cross-section area times prism length. In a triangular prism, the same cross-section also controls the two end faces and the widths of the three rectangular side faces. That means small errors in the triangle dimensions ripple through almost every output. If the triangle is equilateral, the side faces match. If it is scalene, each rectangular face can be different, which changes the surface-area distribution substantially.
Base + height mode is convenient when the cross-section is a right or isosceles triangle and you know the perpendicular height directly. Three-sides mode is more general because it works for any valid triangle, but it relies on Heron's formula to recover the area from side lengths alone. Equilateral mode is the fastest option when all three triangle sides match. Choosing the right mode saves time and reduces the chance of forcing the wrong triangle assumptions into the calculation.
Lateral surface area includes only the three rectangular faces, so it is the quantity to use when the prism ends are open or made from a different material. For a tent, for example, the lateral area helps estimate the fabric for the sloped panels, while the total surface area includes the triangular ends as well. Comparing lateral and total area is a practical way to see how much of the structure is driven by its length versus its cross-section.
Total SA = 2 × (triangle area) + (triangle perimeter) × (prism length). This accounts for the two triangular ends and three rectangular side faces.
The lateral SA includes only the three rectangular side faces: Lateral SA = perimeter of triangle × prism length. It excludes the two triangular ends.
Use Heron's formula to find the triangle area: A = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2. Then compute SA = 2A + (a+b+c) × L.
Volume = (area of the triangular cross-section) × (prism length). It's the same principle as any prism: base area times height (length).
Tents, Toblerone boxes, roof ridges, cheese wedges, triangular rulers, ramps, prism-shaped planters, and architectural glass facades are all triangular prisms. Use this as a practical reminder before finalizing the result.
No. Any side of the triangle can be treated as the base. The height is then measured perpendicular to that base. The final area is the same regardless of which side you choose.