Trapezoidal Prism Volume Calculator
Volume of a trapezoidal prism from its two parallel bases (a, b), trapezoid height (h) and prism length (L) — with base area, surface area and show-your-work steps.
Diagram
Show your work
- Enter values and press Calculate.
Worked examples
Trapezoidal prism volume — FAQ
What is the formula for the volume of a trapezoidal prism?
The volume is V = ((a + b) / 2 × h) × L, where a and b are the two parallel bases of the trapezoid, h is the trapezoid height, and L is the prism length. Example: a = 10 cm, b = 6 cm, h = 4 cm, L = 12 cm gives A = (10 + 6) / 2 × 4 = 32 cm² and V = 32 × 12 = 384 cm³.
How do you calculate the surface area of a trapezoidal prism?
Surface area = 2 × base area + perimeter of the trapezoid × length. With the worked example above (isosceles trapezoid), the leg is √(4² + 2²) = 4.4721 cm, the perimeter is 10 + 6 + 2 × 4.4721 = 24.9443 cm, and the surface area is 2 × 32 + 24.9443 × 12 = 363.3313 cm².
How do you find the slant leg of an isosceles trapezoid?
Use Pythagoras on the half overhang: leg = √(h² + ((b − a) / 2)²). For a = 12 in, b = 4 in, h = 6 in, the leg is √(36 + 16) = √52 = 7.2111 in, giving a volume of 480 in³ and a surface area of 400.2221 in².
What is the difference between a trapezoidal prism and a triangular prism?
The cross-section is different: a trapezoidal prism has a four-sided trapezoid base, while a triangular prism has a three-sided triangle base. The formulas differ accordingly. This calculator is for the trapezoid base only; for a triangular base, use a triangular prism volume calculator (volume-of-a-triangular-prism).
What if the two bases are equal (a = b)?
Then the base is a rectangle and the solid is a rectangular prism: V = a × h × L. Example: a = b = 8 cm, h = 5 cm, L = 20 cm gives V = 800 cm³ and a surface area of 600 cm².
Do I need the isosceles (equal legs) assumption?
No — the volume never needs it. The leg length, trapezoid perimeter, and surface area do, because a general trapezoid’s legs are not determined by a, b, and h alone. Leave “Isosceles trapezoid” checked for the common symmetric case; uncheck it to get volume and base area only.
Free tool by NRTechStudio