Lateral Area Trapezoidal Prism Calculator
Calculate lateral area, surface area, and volume of a trapezoidal prism
Calculate Trapezoidal Prism Properties
Trapezoid Sides
Left side length
Top parallel side
Right side length
Bottom parallel side
Prism Dimensions
Depth of the prism
Perpendicular distance
Calculation Results
Lateral Area Formula: LA = ℓ × (a + b + c + d)
Surface Area Formula: SA = 2 × Base Area + Lateral Area
Base Area Formula: A = h × (b + d) / 2
Geometric Properties
Example Calculation
Swimming Pool Design
Application: Calculate lateral area for pool wall tiles
Side A (left): 4 m
Side B (shallow end): 7 m
Side C (right): 4 m
Side D (deep end): 3 m
Length: 10 m
Height: 7 m
Step-by-Step Calculation
1. Calculate perimeter: P = 4 + 7 + 4 + 3 = 18 m
2. Apply lateral area formula: LA = ℓ × P
3. LA = 10 m × 18 m = 180 m²
Result: 180 m² of tiles needed for walls
Formula Reference
Lateral Area
LA = ℓ × (a + b + c + d)
Length × Perimeter
Base Area
A = h × (b + d) / 2
Trapezoid area formula
Surface Area
SA = 2A + LA
Two bases + lateral area
Volume
V = A × ℓ
Base area × length
Real-World Applications
Swimming Pools
Calculate wall tile area
Construction
Building material estimation
Interior Design
Wall covering calculations
Packaging
Container surface area
Civil Engineering
Bridge component design
Understanding Trapezoidal Prisms
What is a Trapezoidal Prism?
A trapezoidal prism is a three-dimensional geometric shape with two parallel trapezoidal bases connected by rectangular faces. The lateral area refers to the total surface area of these connecting rectangular faces, excluding the top and bottom bases.
Key Components
- •Sides a, b, c, d: The four sides of the trapezoidal cross-section
- •Length (ℓ): The depth or extrusion distance of the prism
- •Height (h): Perpendicular distance between parallel sides
- •Lateral faces: Four rectangular faces connecting the bases
Calculation Methods
Lateral Area:
LA = ℓ × (a + b + c + d)
Multiply length by perimeter of trapezoid
Total Surface Area:
SA = 2 × [h × (b + d) / 2] + LA
Two trapezoidal bases plus lateral area
Note: In the trapezoid, sides b and d are typically the parallel sides (bases), while sides a and c are the non-parallel sides (legs).