How this calculation works
Check the strict triangle inequality and calculate the base area with a stable rearrangement of Heron’s formula. Use prism length perpendicular to the congruent end planes, not an in-plane triangle altitude.
Base area from Heron; V = base area × length; closed area = base perimeter × length + 2 × base areaA worked example
A 3–4–5 m triangular end has area 6 m² and perimeter 12 m. At a perpendicular prism length of 10 m, volume is 60 m³, lateral area 120 m² and closed surface 132 m².
Good to know
A right triangular prism only. No oblique face geometry, taper, wall thickness, material allowance or strength calculation. Triangle side lengths must form a nondegenerate triangle.
Reference: MathWorld: geometry definitions and formulas (opens in a new tab) ↗
Three lengths must form a triangle before a prism exists
The default 3, 4 and 5 m sides form a valid triangular end with area 6 m². A proposed 3, 4 and 8 m end does not: the largest side exceeds the sum of the other two. The tool rejects the base rather than taking a square root of an invalid area expression.
A rearranged Heron calculation is used with high-precision decimal arithmetic to retain near-degenerate side differences. The result is still displayed numerically; a very thin but valid triangle is not silently replaced with a right-triangle assumption.
The triangle area calculator takes a separate base/altitude pair, while this prism page validates three end-side lengths before adding its perpendicular length.
Triangle altitude and prism length are separate dimensions
The prism’s 10 m length is perpendicular between its congruent triangular end planes. Multiplying the 6 m² end area by that length gives 60 m³. The triangle’s derived altitude to its longest side is an in-plane measurement and cannot replace prism length.
For a right prism, the three rectangular side faces have combined area equal to the end perimeter times length. Here that is (3+4+5) × 10 = 120 m². Both triangular end faces add 12 m², giving 132 m² closed area.
Length-only scaling and whole-shape scaling differ
Doubling only prism length doubles volume and lateral area, while the two triangular end areas remain the same. Doubling every length multiplies volume by eight and every surface area by four. The table changes only prism length so that convention stays clear.
The triangle area calculator uses a separate base/altitude input method. The cuboid calculator covers rectangular end geometry. This page assumes a right triangular prism; an oblique prism may have the same volume relationship for perpendicular height but needs different information for its side-face areas.
A few questions, answered
Does the triangular base have to be right-angled?
No. Any positive nondegenerate triangle sides are supported. The prism itself must be right, with its length perpendicular to the end planes.
Why reject equality in the triangle inequality?
Equality collapses the end into a line, rather than a nondegenerate triangular region.
Does lateral area include the two ends?
No. Their combined area is added separately in the closed-surface metric.
Is the derived triangle altitude the prism length?
No. They lie in different directions and serve different parts of the geometry.