Surface Area of a Triangular Prism Calculator
Enter the three sides of the triangular base and the prism's length to compute the total surface area (two triangular ends plus three rectangular faces) and the volume.
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Two triangular bases + three rectangular lateral faces
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Semi-perimeter s = (a + b + c) ÷ 2
(3 + 4 + 5) ÷ 2 = 6 - 2
Triangle area (Heron's formula)
√(6 × 3 × 2 × 1) = 6A = √[s(s−a)(s−b)(s−c)] - 3
Lateral area perimeter × length
(3 + 4 + 5) × 8 = 96 - 4
Total surface area 2·A_tri + lateral
2 × 6 + 96 = 108
How does this calculator work?
A triangular prism's total surface area = 2·A_tri + (a+b+c)·L, where A_tri = √[s(s−a)(s−b)(s−c)] (Heron's formula) and L is the prism length. Volume = A_tri·L. Enter the three base sides and prism length in consistent units.
Formula
How this is calculated
A triangular prism has two congruent triangular bases and three rectangular lateral faces connecting corresponding edges of the two bases. The total surface area is the sum of all five faces: two triangles and three rectangles.
The base triangle area is computed with Heron's formula: first find the semi-perimeter s = (a+b+c)/2, then A = √[s(s−a)(s−b)(s−c)]. This formula works for any valid triangle given only its three side lengths, with no need to know any angle. Each rectangular face has area = (one base edge) × L, and the three rectangles together give the lateral area = (a+b+c)×L — simply the base perimeter times the prism length.
Total surface area = 2A + (a+b+c)L. The volume is base area times length: V = A×L. Inputs must satisfy the triangle inequality (each side less than the sum of the other two), be positive, and share the same unit. Outputs are in square and cubic units of that unit respectively.
Frequently asked questions
Use the direct formula A_triangle = ½ × base × height instead of Heron's formula. You can then compute the lateral area as (sum of all three sides) × L, but you still need all three side lengths for the lateral area. If the triangle is a right triangle, you can recover the hypotenuse from the Pythagorean theorem.
No. This calculator accepts any triangle (acute, obtuse or right) as long as the three sides satisfy the triangle inequality: each side must be strictly less than the sum of the other two. Heron's formula applies to all valid triangles.
Surface area is in the square of whatever unit you enter (e.g., cm²), and volume is in the cube of that unit (e.g., cm³). All four inputs must share the same unit.
Also known as
TG we-Calculate Editorial Team. (2026). Surface Area of a Triangular Prism Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/surface-area-of-a-triangular-prism-calculator
TG we-Calculate Editorial Team. "Surface Area of a Triangular Prism Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/surface-area-of-a-triangular-prism-calculator.
TG we-Calculate Editorial Team, "Surface Area of a Triangular Prism Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/surface-area-of-a-triangular-prism-calculator
@misc{wecalculate_surface_area_of_a_triangular_prism_calculator, title = {Surface Area of a Triangular Prism Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/surface-area-of-a-triangular-prism-calculator}}, year = {2026}, note = {TG we-Calculate} }
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