Volume of a Trapezoidal Prism Calculator
Calculate volume and surface area of trapezoidal prisms using base lengths, height, and length
Calculate Trapezoidal Prism Volume
Length of the shorter parallel side of the trapezoid
Length of the longer parallel side of the trapezoid
Perpendicular distance between the parallel bases
Length of the prism (depth dimension)
Trapezoidal Prism Properties
Volume
Formulas Used
Volume: V = ((b + B) / 2) × h × ℓ
Trapezoid Area: A = ((b + B) / 2) × h
Lateral Area: LA = (b + B + 2h) × ℓ
Total Surface Area: TSA = 2A + LA
Example Calculation
Swimming Pool Example
Problem: A swimming pool has a trapezoidal cross-section with a shallow end of 3m, deep end of 8m, height of 2m, and length of 25m. What is its volume?
Given:
Short base (b) = 3 m
Long base (B) = 8 m
Height (h) = 2 m
Length (ℓ) = 25 m
Solution
Step 1: Apply trapezoidal prism volume formula
V = ((b + B) / 2) × h × ℓ
Step 2: Substitute values
V = ((3 + 8) / 2) × 2 × 25
V = (11 / 2) × 2 × 25
V = 5.5 × 2 × 25
V = 275 m³
Trapezoidal Prism Properties
Trapezoid Base
Has two parallel sides of different lengths
Uniform Cross-Section
Same trapezoidal shape throughout its length
6 Faces
2 trapezoidal bases + 4 rectangular sides
Quick Formulas
Real-World Applications
Swimming pool design and construction
Road and highway embankments
Architectural structures and beams
Water channels and irrigation systems
Industrial container and tank design
Understanding Trapezoidal Prism Volume and Surface Area
What is a Trapezoidal Prism?
A trapezoidal prism is a 3D geometric shape with two parallel trapezoidal bases connected by four rectangular faces. The trapezoid has two parallel sides (bases) of different lengths, and the prism maintains this cross-sectional shape along its entire length.
Volume Formula Explanation
The volume is calculated by finding the area of the trapezoidal base and multiplying by the length (depth) of the prism:
Trapezoid area: A = ((b + B) / 2) × h
Volume: V = A × ℓ = ((b + B) / 2) × h × ℓ
Key Variables
- b: Length of short base (shorter parallel side)
- B: Length of long base (longer parallel side)
- h: Height (perpendicular distance between bases)
- ℓ: Length/depth of the prism
Surface Area Components
A trapezoidal prism has 6 faces total:
- •2 Trapezoidal bases: Each with area ((b + B) / 2) × h
- •4 Rectangular sides: With areas b×ℓ, B×ℓ, h×ℓ, h×ℓ
Surface Area Calculation
Lateral Area = (b + B + 2h) × ℓ
Total Surface Area = 2 × Trapezoid Area + Lateral Area
TSA = 2 × ((b + B) / 2) × h + (b + B + 2h) × ℓ
Important: Make sure all measurements use the same units before calculating. The calculator automatically handles unit conversions for accurate results.
Common Applications and Examples
Swimming Pools
Pool volumes for chemical treatment and construction:
Deep end: 8m
Width: 2m
Length: 25m
Volume: 275 m³
Road Embankments
Calculate material needs for construction:
Bottom width: 20m
Height: 5m
Length: 1000m
Volume: 75,000 m³
Water Channels
Irrigation and drainage system design:
Bottom width: 1m
Depth: 0.8m
Length: 500m
Volume: 600 m³