Triangular Prism Calculator
Calculate the volume, base area, lateral and total surface area of a triangular prism — from the three triangle sides using Heron's formula, or from base and height.
Frequently Asked Questions
How do you calculate the volume of a triangular prism?
V = triangle area × prism length. Find the triangle area either as ½ × base × height, or from three sides with Heron's formula: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. A 3-4-5 triangle (area 6) with prism length 10 gives V = 60.
How do you find the surface area of a triangular prism?
SA = 2 × triangle area + perimeter × length — the two triangular ends plus three rectangles whose combined width is the triangle's perimeter. For the 3-4-5 triangle with length 10: SA = 2×6 + 12×10 = 132 square units.
What is Heron's formula and when do I use it?
Heron's formula computes a triangle's area from its three side lengths alone — no height needed: A = √(s(s−a)(s−b)(s−c)) with s the semi-perimeter. It is ideal when you can measure the sides but not the height, as with land plots or cut materials. The sides must satisfy the triangle inequality (each pair must sum to more than the third side).
Where are triangular prisms used in real life?
Roof structures (the classic gable roof encloses a triangular prism), optical prisms that split light, tent designs, chocolate packaging (Toblerone is the famous example), ramps, and structural supports. Calculating their volume and surface area matters for material estimates and capacity.