Surface Area of a Trapezoidal Prism Calculator
Get the total and lateral surface area of a trapezoidal prism from its two parallel bases, height, legs, and length. Works in any consistent unit (inches, feet, cm), and an isosceles mode computes the slant legs for you.
Example: with Bottom base of trapezoid (a) 11 · Top base of trapezoid (b) 5 · Trapezoid height (h) 4 · Legs (slant sides) Isosceles — compute legs from a, b, h · Leg c (manual mode) 5 → Total surface area: 324 square units.
- Lateral area (4 rectangles)260 square units
- One trapezoid face32 square units each (two faces = 64)
- Trapezoid perimeter26 units (legs 5 and 5)
Computed by the calculator below using its default values. Change any input to see your own numbers.
SA = (a + b)h + (a + b + c + d)L — two trapezoid ends plus perimeter × length of wall. A right prism is assumed.
How the surface area breaks down
A trapezoidal prism has six faces: two identical trapezoid ends and four rectangles wrapped around them. Each rectangle is as long as the prism (L) and as wide as one side of the trapezoid, so the four rectangles together cover perimeter × L. Add the two trapezoid ends at (a + b)/2 × h each and you have the whole formula: SA = (a + b)h + (a + b + c + d)L.
The lateral area is just the rectangular wrap — useful on its own when the ends do not count, like an open trough, a duct run, or a ramp core that will be capped separately.
Getting the legs right
The legs c and d are the two slanted sides of the trapezoid, and they are usually the numbers people do not have. If your trapezoid is isosceles (symmetric, the common textbook case), each leg is the hypotenuse of a right triangle with height h and horizontal run (a − b)/2, so c = √(h² + ((a − b)/2)²). The default mode computes that for you. If the trapezoid leans, the two legs differ — switch to manual mode and enter both.
How it’s calculated
SA = (a + b) × h + (a + b + c + d) × L: two trapezoid faces of area (a + b)/2 × h each, plus four rectangles whose combined width is the trapezoid perimeter and whose length is L. Isosceles mode sets both legs to c = √(h² + ((a − b)/2)²). All inputs must share one unit; outputs are in that unit squared, rounded to 3 decimals.
Assumes a right prism — the trapezoid cross-section is constant and the ends sit perpendicular to the length; an oblique (skewed) prism has more lateral area than this.
Surface-area formulas for common prisms
| Solid | Total surface area |
|---|---|
| Rectangular prism | 2(lw + lh + wh) |
| Cube | 6s² |
| Triangular prism | bh + (s₁ + s₂ + s₃)L |
| Trapezoidal prism | (a + b)h + (a + b + c + d)L |
Standard mensuration formulas — two base areas plus perimeter × length; this page computes the trapezoidal row.
Common mistakes
- Using a slant leg as the trapezoid height h — h is the perpendicular distance between the two parallel bases.
- Counting only one trapezoid face; a prism has two identical ends.
- Mixing up the prism length L with the trapezoid height h — L runs along the solid, h across the end face.
- Applying the isosceles leg shortcut to a trapezoid that leans; unequal legs must be entered individually.
Frequently asked questions
What is the surface area formula for a trapezoidal prism?
SA = (a + b) × h + (a + b + c + d) × L. The first term is the two trapezoid ends (each (a + b)/2 × h), and the second is the four rectangles: the trapezoid's perimeter times the prism length L.
What is the lateral surface area?
The four rectangular sides only — perimeter of the trapezoid times prism length, with the two trapezoid ends left off. Use it for open-ended shapes like troughs and duct sections.
How do I find the legs if I only know the bases and height?
Only when the trapezoid is isosceles: each leg is √(h² + ((a − b)/2)²), from the right triangle at each end. This page's isosceles mode applies that automatically; a leaning trapezoid needs both legs measured.
Does it matter which base I call a and which b?
No. Both the area term (a + b)/2 × h and the perimeter a + b + c + d are symmetric in a and b, so swapping them changes nothing.