Lateral Area Trapezoidal Prism Calculator

Background.

A trapezoidal prism is a solid whose cross-section is a trapezoid all the way along: a wedge-shaped gift box, a planter that flares towards the top, a length of trapezoid-section duct, a concrete kerb or a drainage channel. Its surface splits naturally into two parts, the two trapezoid ends and the four rectangular faces that run between them. The lateral area is the second part only.

That split matters in practice because the jobs differ. Cladding a duct, painting the long faces of a beam, wrapping a band of paper around a box or estimating the liner for a channel all concern the sides, while the ends are often open, hidden against a wall or made from a different material.

The calculation is unusually forgiving. Unwrap the four side faces and they lay flat as one long rectangle: its width is the distance around the trapezoid, and its length is the length of the prism. So the lateral area is simply the perimeter of the trapezoid times the prism length. The angles of the sloping sides, the height of the trapezoid and which pair of sides is parallel never enter the arithmetic.

Two things to keep in mind. The rule holds for a right prism, where the side faces meet the ends at right angles; an oblique prism, leaning like a pushed-over stack of cards, needs a different treatment. And the page accepts any four positive lengths without checking that they can actually close up into a trapezoid, so it is worth sketching the end shape first.

What is lateral area trapezoidal prism calculator?

The lateral surface area of a trapezoidal prism is the combined area of its four rectangular side faces, excluding the two trapezoid-shaped ends. For a right prism each face is a rectangle whose width is one side of the trapezoid and whose length is the prism length, so the total equals the trapezoid's perimeter multiplied by that length. The result is in square units of whatever length unit the sides were measured in.

How to use this calculator.

1. 01Measure the four sides of the trapezoid end: the two parallel sides and the two sloping legs. Enter them as sides a, b, c and d in any order, since only their sum is used.
2. 02Enter the prism length, the distance from one trapezoid end to the other, in the same unit as the sides.
3. 03Read the lateral surface area in square units. Centimetres in give square centimetres out; metres in give square metres.
4. 04If one side face is open, as with a trough or channel, subtract that side's width times the prism length from the result.

The formula.

Lateral area = (a + b + c + d) × L. The bracket is the perimeter of the trapezoid end, the sum of its two parallel sides and two legs; L is the length of the prism, measured along its edges. Each of the four side faces is a rectangle with one trapezoid side as its width and L as its length, so adding the four rectangle areas, aL + bL + cL + dL, gives the same total. No height, angle or constant appears. Because every side and the length enter as straight sums and products, doubling the length doubles the area, and a 1-unit increase in any one side adds exactly L square units. To get the total surface area, add twice the area of the trapezoid, which does need its height.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.