Triangular Prism Volume & Surface Area Calculator
Find the volume and surface area of a triangular prism from its three base-triangle sides and its length.
How it works
Cross-section area = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 · V = area · length · Surface area = 2·area + (a+b+c)·length
A triangular prism is a triangle extruded along a straight length. Its volume is the area of that triangular cross-section multiplied by the prism’s length. The cross-section area comes from Heron’s formula, which needs only the three side lengths — no height or angle. The surface area adds the two triangular ends (2 × area) to the three rectangular sides, whose combined area is the triangle’s perimeter times the length.
Worked example
For a 3-4-5 right-triangle cross-section and a length of 10 units: s = 6, area = √(6·3·2·1) = √36 = 6 units²; volume = 6 · 10 = 60 units³; surface area = 2·6 + (3+4+5)·10 = 12 + 120 = 132 units².
Sources: Triangular prism — Wolfram MathWorld
Frequently asked questions
Why use Heron’s formula instead of ½ · base · height?
Heron’s formula needs only the three side lengths, which are usually easier to measure than the triangle’s perpendicular height. Both give the same cross-section area when the height is known.
What if my three sides do not form a triangle?
A valid triangle requires each side to be shorter than the sum of the other two. If that fails, no prism exists and the calculator asks for valid sides.
Does the surface area include the two ends?
Yes. The total surface area counts both triangular ends plus the three rectangular side faces. If the ends are open, subtract 2 × the cross-section area.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.