The Trapezoidal Prism Surface Area Calculator calculates the total surface area of a prism whose ends are trapezoids, such as a trough, a ridge, or a tapered channel.
Trapezoidal Prism Surface Area Calculator
Surface area of a trapezoidal prism from the trapezoid bases, height and legs, or an isosceles trapezoid.
It adds the two trapezoid ends, (a + b) × h, to the four rectangular sides, which equal the trapezoid perimeter times the prism length. For an isosceles trapezoid the calculator works out the leg length for you; for any other trapezoid you enter both legs.
Formula
A = 2 × ((a + b) ÷ 2) × h + (a + b + c + d) × L
which simplifies to A = (a + b) × h + (a + b + c + d) × L.
For an isosceles trapezoid (equal legs):
c = √(h² + ((a − b) ÷ 2)²) and A = (a + b) × h + (a + b + 2c) × L
Where:
- a = bottom base (longer parallel side), b = top base
- h = height of the trapezoid (distance between the bases)
- c, d = the two legs (slanted sides)
- L = prism length
How the Calculation Works
Step 1: Find the area of one trapezoid end: (a + b) ÷ 2 × h. There are two ends, so the ends together give (a + b) × h.
Step 2: Find the lateral area: add the four sides of the trapezoid (its perimeter) and multiply by the prism length.
Step 3: Add the two results to get the total surface area.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| a, b | Parallel sides (bases) of the trapezoid | cm, m, in, ft |
| h | Trapezoid height | cm, m, in, ft |
| c, d | Legs of the trapezoid | cm, m, in, ft |
| L | Prism length | cm, m, in, ft |
| A | Total surface area | cm², m², in², ft² |
Example Calculation
Given: isosceles trapezoid with a = 10 cm, b = 6 cm, h = 4 cm; prism length L = 12 cm
Leg length: c = √(4² + ((10 − 6) ÷ 2)²) = √(16 + 4) = √20 ≈ 4.472 cm
Two ends: (10 + 6) × 4 = 64 cm²
Lateral area: (10 + 6 + 2 × 4.472) × 12 = 24.944 × 12 ≈ 299.33 cm²
Result: A ≈ 64 + 299.33 = 363.33 cm²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 ft² | 144 in² |
| 1 m² | 10.7639 ft² |
Shape Properties
A trapezoidal prism has 6 faces: 2 trapezoids and 4 rectangles, plus 12 edges and 8 vertices. When a = b, the trapezoid becomes a rectangle and the shape is a rectangular prism.
Dimensions Explained
Trapezoid height vs leg length
The height is measured straight between the parallel sides. The legs are the slanted sides and are always at least as long as the height. Mixing them up is the most common error.
When to use “Any trapezoid”
If the two slanted sides differ (for example a channel with one vertical wall), use the Any trapezoid mode and enter both legs.
Frequently Asked Questions
How do you find the surface area of a trapezoidal prism?
Add the areas of the two trapezoid ends to the four rectangles: A = (a + b) × h + (a + b + c + d) × L.
What is the lateral area of a trapezoidal prism?
It is the perimeter of the trapezoid times the prism length: (a + b + c + d) × L.
How do you find the leg of an isosceles trapezoid?
Use c = √(h² + ((a − b) ÷ 2)²). The calculator does this automatically in Isosceles mode.
How many faces does a trapezoidal prism have?
Six: two trapezoidal faces and four rectangular faces.
What is the volume of a trapezoidal prism?
Volume = trapezoid area × length = ((a + b) ÷ 2) × h × L. For the example above that is 8 × 4 × 12 = 384 cm³.