Trapezoidal Prism Volume Calculator

What Is a Trapezoidal Prism?

A trapezoidal prism is a 3D solid whose cross-section is a trapezoid. It has a short base $b$, long base $B$, trapezoid height $h$, and prism length $\ell$. Volume equals the trapezoid base area times the prism length.

Trapezoidal Prism Volume Formula

$$V = \frac{(b + B)}{2} \times h \times \ell$$

The term $\frac{(b+B)}{2} \times h$ is the trapezoid cross-sectional area, multiplied by prism length $\ell$.

Worked Example

A prism has short base 4 m, long base 7 m, height 3.5 m, and length 10 m. Base area $= \frac{4+7}{2} \times 3.5 = 19.25$ m². Volume $= 19.25 \times 10 = 192.5$ m³.

Frequently Asked Questions

How is trapezoidal prism volume calculated?

Find the trapezoid cross-section area $\frac{(b+B)}{2} \times h$, then multiply by prism length $\ell$. Our calculator does both steps with a breakdown.

Can volume be negative?

No. Volume is always non-negative. All input dimensions must be positive numbers.

What is the difference between height and length?

Height $h$ is the perpendicular distance between the two parallel bases of the trapezoid face. Length $\ell$ is how far the prism extends perpendicular to that face.

How does this relate to a rectangular prism?

When $b = B$, the trapezoid becomes a rectangle and the formula reduces to $V = b \times h \times \ell$, the standard rectangular prism volume.

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Trapezoidal Prism Volume Calculator

What Is a Trapezoidal Prism?

Trapezoidal Prism Volume Formula

Worked Example

Frequently Asked Questions

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