📐 Volume of a Trapezoidal Prism Calculator
Calculate the volume of a trapezoidal prism
Trapezoid Base Dimensions
How to Use This Calculator
Enter Trapezoid Base Dimensions
Input the two base lengths (b₁ and b₂) and two leg lengths (l₁ and l₂) of the trapezoidal base. The bases are the parallel sides, and legs are the non-parallel sides.
Enter Prism Height
Input the height (h) of the prism, which is the perpendicular distance between the two trapezoidal bases (not the height of the trapezoid itself).
Get Volume
Click "Calculate Volume" to get the volume using the formula Volume = Base Area × Height. The calculator shows both the trapezoidal base area and the final volume.
Formulas
Base Area = (1/2) × (b₁ + b₂) × h_t
Where h_t is the perpendicular height between the two parallel bases
Volume = Base Area × Prism Height
Trapezoid area multiplied by prism height
Where:
- b₁ = length of first base (parallel side)
- b₂ = length of second base (parallel side)
- l₁, l₂ = lengths of non-parallel sides (legs)
- h_t = perpendicular height between the two parallel bases of the trapezoid
- h = height of the prism (perpendicular distance between trapezoidal bases)
- Base Area = area of the trapezoidal base
- Volume = space inside the prism
Note: For an isosceles trapezoid, the height can be calculated using: h_t = √(l² - ((b₂-b₁)/2)²), where l is the leg length. For non-isosceles trapezoids, the calculation may vary.
Example 1: Trapezoidal prism with bases b₁=8, b₂=12, legs l₁=5, l₂=5 (isosceles), prism height=10
For isosceles trapezoid: h_t = √(5² - ((12-8)/2)²) = √(25 - 4) = √21 ≈ 4.58
Base Area = (1/2) × (8 + 12) × 4.58 = 10 × 4.58 = 45.8 units²
Volume = 45.8 × 10 = 458 units³
Example 2: Trapezoidal prism with bases b₁=6, b₂=10, legs l₁=4, l₂=4, prism height=7
h_t = √(4² - ((10-6)/2)²) = √(16 - 4) = √12 ≈ 3.46
Base Area = (1/2) × (6 + 10) × 3.46 = 8 × 3.46 = 27.68 units²
Volume = 27.68 × 7 = 193.76 units³
About Volume of a Trapezoidal Prism Calculator
A trapezoidal prism is a 3D shape with two parallel, identical trapezoidal bases connected by rectangular faces. The volume is calculated by multiplying the area of the trapezoidal base by the height of the prism. This calculator finds the volume using the trapezoid area formula and prism volume relationship.
When to Use This Calculator
- Architecture: Calculate volumes for trapezoidal prism buildings or structures
- Engineering: Determine material volumes for trapezoidal prism components
- Construction: Estimate concrete, sand, or other materials needed for trapezoidal prism structures
- Mathematics Education: Teach students about 3D geometry and trapezoidal prisms
- Design: Plan volumes for trapezoidal prism objects
- Packaging: Calculate capacity of trapezoidal prism containers
Why Use Our Calculator?
- ✅ Flexible Input: Works with any trapezoid dimensions
- ✅ Instant Results: Get accurate volume calculations immediately
- ✅ Base Area Included: Shows trapezoidal base area calculation
- ✅ Step-by-Step Display: See the formulas applied with your values
- ✅ 100% Accurate: Uses precise mathematical formulas
- ✅ Completely Free: No registration required
Understanding Trapezoidal Prisms
A trapezoidal prism consists of:
- Two Trapezoidal Bases: Parallel, identical trapezoids
- Rectangular Faces: Connecting corresponding sides of the bases
- Base Area: Area of trapezoid = (1/2) × (base1 + base2) × height_of_trapezoid
- Volume: Base area × prism height (space inside)
- Trapezoid Height: Perpendicular distance between the two parallel bases of the trapezoid (not the prism height)
Real-World Applications
Construction: A trapezoidal prism foundation has bases 8 m and 12 m, legs 5 m each, and prism height 3 m. Base area ≈ 45.80 m², Volume = 137.40 m³ (concrete needed).
Engineering: A trapezoidal storage container with bases 6 m and 10 m, legs 4 m each, and height 5 m has base area ≈ 27.68 m² and volume = 138.40 m³ (storage capacity).
Packaging: A trapezoidal gift box with bases 15 cm and 20 cm, legs 8 cm each, and height 10 cm has base area ≈ 140 cm² and volume = 1,400 cm³ (capacity).
Frequently Asked Questions
What is a trapezoidal prism?
A trapezoidal prism is a 3D shape with two parallel, identical trapezoidal bases connected by rectangular faces. The bases are trapezoids (quadrilaterals with one pair of parallel sides), and the prism extends perpendicularly from these bases.
What's the difference between trapezoid height and prism height?
Trapezoid height (h_t) is the perpendicular distance between the two parallel bases of the trapezoid itself. Prism height (h) is the perpendicular distance between the two trapezoidal bases of the 3D prism. They are different measurements!
How do I calculate the trapezoid height if I only know the sides?
For an isosceles trapezoid (equal legs), use: h_t = √(l² - ((b₂-b₁)/2)²), where l is the leg length. For non-isosceles trapezoids, you may need additional information (like angles) or the height itself to calculate area accurately.
Can I use this for a right trapezoidal prism?
Yes! A right trapezoidal prism is one where the edges are perpendicular to the bases. The volume formula is the same: Volume = Base Area × Height. The calculator works for both right and oblique trapezoidal prisms.
What if the trapezoid is isosceles?
An isosceles trapezoid has equal legs (l₁ = l₂). The calculator handles this case perfectly - just enter the same value for both legs. The height calculation becomes simpler with equal legs.
How is this different from a rectangular prism?
A rectangular prism has rectangular bases (all angles are 90°). A trapezoidal prism has trapezoidal bases (only one pair of sides parallel). The volume formula is similar (Base Area × Height), but the base area calculation differs: rectangle = length × width, trapezoid = (1/2) × (b₁ + b₂) × height.