How this calculator works
A triangular prism has two identical triangular ends joined by three rectangular sides. The total surface area is the two ends plus the three rectangles. The rectangle widths are the three triangle sides, and all three rectangles share the prism length, so together they form one large rectangle whose width is the triangle perimeter. The end area comes from Heron's formula, which needs only the three side lengths. The three sides must be able to close into a triangle, otherwise no prism exists.
Formula
s = (a + b + c)/2; end area = √(s(s-a)(s-b)(s-c)); lateral area = (a + b + c) × length; total area = 2 × end area + lateral area; volume = end area × length.
Worked example
A 3-4-5 triangle has an end area of 6 m² and a perimeter of 12 m. With a prism length of 10 m, the lateral area is 120 m² and the total surface area is 2 × 6 + 120 = 132 m². The volume is 6 × 10 = 60 m³.
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Frequently asked questions
Why does the triangle inequality matter?
Three lengths can only form a triangle if each one is shorter than the sum of the other two. A set such as 1 m, 2 m and 5 m cannot close, so it has no area and no prism can be built from it.
What if I only know the base and height of the triangle?
Compute the end area as half the base times the height, then add the perimeter times the prism length. This calculator uses three sides so it also works when the height is not known.
Which faces does the total include?
The total counts both triangular ends and all three rectangular sides. The lateral area leaves out the ends and covers only the rectangles.