Trapezoidal Prism Volume Calculator — V = ½(a+b)×h×L
Find the volume, base area, lateral surface area, and total surface area of a trapezoidal prism. Enter the two parallel sides of the trapezoidal cross-section, its perpendicular height, and the length (depth) of the prism. Leg lengths are optional — leave blank for an isosceles cross-section.
V = ½ × (a + b) × h × L
- 1
Average of the bases (a + b) ÷ 2
(6 + 10) ÷ 2 = 8 - 2
Trapezoid cross-section area
8 × 4 = 32Base area = midsegment × perpendicular height of the trapezoid. - 3
Volume = base area × prism length
32 × 8 = 256
How does this calculator work?
Volume of a trapezoidal prism = ½ × (a + b) × h × L, where a and b are the parallel bases, h is the trapezoid height, and L is the prism length. Total surface area = (a + b + c + d) × L + (a + b) × h, with the legs computed automatically if left blank.
Formula
How this is calculated
A trapezoidal prism is a three-dimensional solid whose two end faces are congruent trapezoids and whose four lateral faces are rectangles. The volume equals the area of the trapezoidal cross-section multiplied by the prism length: V = ½ × (a + b) × h × L, where a and b are the parallel bases and h is the perpendicular height of the trapezoid.
The lateral surface area is the total area of the four rectangular side faces: LA = (a + b + c + d) × L, where c and d are the non-parallel legs of the trapezoid. If you leave the legs blank the calculator assumes an isosceles cross-section and computes each leg as √(h² + ((b − a)/2)²) using the Pythagorean theorem on the horizontal overhang.
The total surface area adds both trapezoidal end faces: TSA = LA + 2 × ½ × (a + b) × h. All inputs must be in the same unit; the volume will be in that unit cubed and areas in that unit squared.
Frequently asked questions
The trapezoid height h is the perpendicular distance between the two parallel sides (a and b) within the trapezoidal cross-section. The prism length L is the depth of the solid — the distance between the two trapezoidal end faces.
No — the volume only depends on the base areas: V = ½(a+b)×h×L. The leg lengths are needed only for the lateral and total surface areas. If omitted, the calculator assumes an isosceles trapezoid and computes them automatically.
A rectangular prism has a rectangular cross-section (a = b, right-angle legs). A trapezoidal prism has a trapezoidal cross-section with two bases of different lengths. When a = b the trapezoid degenerates to a rectangle and the formulas reduce to the cuboid formulas.
Also known as
TG we-Calculate Editorial Team. (2026). Trapezoidal Prism Volume Calculator — V = ½(a+b)×h×L [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/trapezoidal-prism-volume-calculator
TG we-Calculate Editorial Team. "Trapezoidal Prism Volume Calculator — V = ½(a+b)×h×L." TG we-Calculate. 2026. https://we-calculate.com/calculator/trapezoidal-prism-volume-calculator.
TG we-Calculate Editorial Team, "Trapezoidal Prism Volume Calculator — V = ½(a+b)×h×L," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/trapezoidal-prism-volume-calculator
@misc{wecalculate_trapezoidal_prism_volume_calculator, title = {Trapezoidal Prism Volume Calculator — V = ½(a+b)×h×L}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/trapezoidal-prism-volume-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?