Trapezoidal prisms are common in construction – drainage channels, embankments, dams, some roofs and gift boxes. The lateral area tells you how much lining or cladding the sides need.
How to use the Lateral Area of a Trapezoidal Prism Calculator
- Base a (bottom)
- Base b (top)
- Leg c
- Leg d
- Trapezoid height h
- Prism length ℓ
Results update as you type, and everything is calculated in your browser.
How it works
Enter the two parallel sides a and b, the legs c and d, the height h of the trapezoid and the length ℓ of the prism.
Inputs explained
| Field | What to enter |
|---|---|
| Base a (bottom) | Units: cm, m, mm, in, ft, yd … |
| Base b (top) | Units: cm, m, mm, in, ft, yd … |
| Leg c | Units: cm, m, mm, in, ft, yd … |
| Leg d | Units: cm, m, mm, in, ft, yd … |
| Trapezoid height h | Units: cm, m, mm, in, ft, yd … |
| Prism length ℓ | Units: cm, m, mm, in, ft, yd … |
What each result means
- Lateral area = ([Base a (bottom)] + [Base b (top)] + [Leg c] + [Leg d])×[Prism length ℓ]
- Base area (one end) = ([Base a (bottom)] + [Base b (top)])×[Trapezoid height h]÷2
- Total surface area = [Lateral area] + 2×[Base area (one end)]
- Volume = [Base area (one end)]×[Prism length ℓ]
Example values
How the main result changes when Base a changes and everything else stays at the example values above:
| Base a (bottom) (cm) | Lateral area (cm²) |
|---|---|
| 5 | 420 |
| 7.5 | 470 |
| 10 | 520 |
| 12.5 | 570 |
| 15 | 620 |
| 20 | 720 |
Formula
Lateral area = (a + b + c + d)·ℓ, base area = (a + b)·h/2
Total = lateral + 2·base, V = base·ℓ
Worked example
Inputs — Base a (bottom): 10 cm; Base b (top): 6 cm; Leg c: 5 cm; Leg d: 5 cm; Trapezoid height h: 4.583 cm; Prism length ℓ: 20 cm.
Results — Lateral area = 520 cm²; Base area (one end) = 36.664 cm²; Total surface area = 593.328 cm²; Volume = 733.28 cm³.
Key terms
- Lateral face
- A side face of a prism.
Frequently asked questions
What is a lateral area?
The area of the side faces, excluding the two ends.
Are the legs always equal?
Only for an isosceles trapezoid.
How do I find the height from the sides?
Split into a rectangle and two right triangles.
What is the volume?
Trapezoid area × length.