Last updated October 10, 2026 · Report an error
A trapezoidal prism is a solid with a trapezoid as its constant cross-section, extended along a straight length — think of a highway embankment, a drainage channel, or a retaining wall's cross-section extended along its run. Its volume, like that of any prism, is its cross-sectional area multiplied by the prism's length, which makes this shape common in civil engineering and earthworks calculations (estimating soil or concrete volume for embankments, canals, and foundation footings whose cross-section tapers from a wider top or bottom).
How it works
Enter the trapezoid's two parallel sides (a and b) and its height (the perpendicular distance between those two parallel sides), plus the prism's length. The calculator first finds the trapezoid's cross-sectional area using the standard trapezoid area formula, (a+b)/2 × h, then multiplies that area by the prism length to get the total volume — exactly the same "cross-sectional area × length" logic used for any prism.
- Enter trapezoid parallel side a.
- Enter trapezoid parallel side b.
- Enter trapezoid height.
- Enter prism length.
- Click Calculate to see your results.
Examples
Sides 4 and 6, trapezoid height 3, prism length 10
Trapezoid area = (4+6)/2 × 3 = 5 × 3 = 15. Volume = 15 × 10 = 150.
Sides 8 and 12, trapezoid height 5, prism length 20
Trapezoid area = (8+12)/2 × 5 = 10 × 5 = 50. Volume = 50 × 20 = 1000.
Common mistakes to avoid
- Confusing the trapezoid's height (the perpendicular distance between the parallel sides) with the prism's length (the extension distance).
- Forgetting to divide by 2 in the trapezoid area formula (computing (a+b)×h instead of (a+b)/2×h).
- Assuming the cross-section must taper along the prism's length — a true trapezoidal prism keeps the same trapezoid shape all the way through.