Lateral Area of a Trapezoidal Prism Calculator
Type the four sides of the trapezoid base (two parallel sides a, b and two legs c, d) and the prism length L — the calculator returns the lateral surface area and each of the four rectangular face areas.
Lateral surface area (LA = (a + b + c + d) · L)
210 square units
- Base perimeter (a + b + c + d)
- 21
- Face on side a (a · L)
- 50
- Face on side b (b · L)
- 80
- Face on leg c (c · L)
- 40
- Face on leg d (d · L)
- 40
A trapezoidal prism has two congruent trapezoid bases and four rectangular lateral faces — one for each side of the trapezoid. Because each lateral face is a rectangle with one side equal to a trapezoid edge and the other equal to the prism length L, the total lateral (side) area is simply the perimeter of the trapezoid multiplied by L: LA = (a + b + c + d) · L. The trapezoid height does not appear — it only affects the base area, not the lateral area.
How to use this calculator
Enter the four sides of the trapezoid base — the two parallel sides a and b, and the two non-parallel sides (legs) c and d — plus the length L of the prism (the distance between the two trapezoid faces). Use any consistent linear unit: centimetres, metres, inches, or feet. Areas come out in the corresponding squared unit (cm², m², in², ft²). The trapezoid height is not required for lateral area, only its perimeter.
How the calculation works
The lateral area of any right prism equals the perimeter of its base times the length of the prism. A trapezoidal prism has a trapezoid base with four sides — parallel sides a and b, plus legs c and d — so its perimeter is a + b + c + d. The four lateral faces are each rectangles: one face has area a·L, another b·L, and the two legs give c·L and d·L. Adding them gives LA = (a + b + c + d) · L, which is the compact formula shown at the top. This formula is exact for a right prism, where the lateral edges are perpendicular to the base; for an oblique prism you would use the slant length rather than L.
Worked example
A trapezoidal prism has parallel sides a = 5 and b = 8, legs c = 4 and d = 4, and prism length L = 10 — all in centimetres. The trapezoid perimeter is 5 + 8 + 4 + 4 = 21 cm. Lateral area LA = 21 · 10 = 210 cm². Broken down by face: the side on a is 5·10 = 50 cm², the side on b is 8·10 = 80 cm², and each leg contributes 4·10 = 40 cm², summing to 50 + 80 + 40 + 40 = 210 cm² — matching the compact formula.
Frequently asked questions
What is the formula for the lateral area of a trapezoidal prism?
Lateral area = (a + b + c + d) · L, where a and b are the parallel sides of the trapezoid base, c and d are its two legs (non-parallel sides), and L is the length of the prism between its two trapezoid faces. Equivalently, LA = P · L where P is the perimeter of the trapezoid.
What is lateral area — is it the same as total surface area?
No. Lateral area is only the four rectangular side faces of the prism — the faces that wrap around it. Total surface area also includes the two trapezoid end faces (top and bottom). If you need total surface area, add 2 · (trapezoid base area). Lateral area on its own is what you use for tasks like wrapping, painting, or labelling only the sides.
Do I need the height of the trapezoid?
Not for lateral area. Lateral area of a right prism depends only on the base perimeter and the prism length, so only the four side lengths and L are needed. The trapezoid height enters if you want the total surface area, because it is used to compute the two trapezoid end faces via A = ½·(a + b)·h.
Does this formula work for an oblique trapezoidal prism?
The formula LA = perimeter · L assumes a right prism, where the lateral edges are perpendicular to the base. For an oblique prism you replace L with the perpendicular slant height of each rectangular face — in general each lateral face becomes a parallelogram rather than a rectangle. Most textbook problems, and this calculator, assume the right-prism case.
What units does the answer come out in?
Lateral area comes out in the square of whatever linear unit you use. If you entered lengths in centimetres, the answer is in cm². Metres → m². Inches → in². Feet → ft². All five inputs must use the same unit; the calculator does not convert between units.
What is a trapezoidal prism?
A trapezoidal prism is a solid with two parallel congruent trapezoid faces (the bases) connected by four rectangular side faces. It has 6 faces, 12 edges, and 8 vertices. Real-world examples include some concrete kerbs, ridge beams, certain glass paperweights, and roof rafters cut with a trapezoidal cross-section.