# Lateral Area of a Trapezoidal Prism Calculator

URL: https://speedycalculator.com/calculators/math/lateral-area-trapezoidal-prism/
Last updated: 2026-10-30

> The lateral area of a trapezoidal prism calculator finds the lateral (side) area, the base area, the total surface area and the volume of a prism whose base is a trapezoid.

## Inputs

- Base a (bottom) (cm, m, mm, in, ft, yd, km, mi)
- Base b (top) (cm, m, mm, in, ft, yd, km, mi)
- Leg c (cm, m, mm, in, ft, yd, km, mi)
- Leg d (cm, m, mm, in, ft, yd, km, mi)
- Trapezoid height h (cm, m, mm, in, ft, yd, km, mi)
- Prism length ℓ (cm, m, mm, in, ft, yd, km, mi)

## Results

- Lateral area
- Base area (one end)
- Total surface area
- Volume

## Formula

```
Lateral area = (a + b + c + d)·ℓ,  base area = (a + b)·h/2
Total = lateral + 2·base,  V = base·ℓ
```

## Explanation

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

FieldWhat to enterBase a (bottom)Units: cm, m, mm, in, ft, yd …Base b (top)Units: cm, m, mm, in, ft, yd …Leg cUnits: cm, m, mm, in, ft, yd …Leg dUnits: cm, m, mm, in, ft, yd …Trapezoid height hUnits: cm, m, mm, in, ft, yd …Prism length ℓUnits: 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)54207.54701052012.55701562020720

## 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.

## FAQ

**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.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Solid geometry](https://mathworld.wolfram.com/SolidGeometry.html)