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Calculate volume and surface area of trapezoidal prisms with step-by-step solutions
Volume: V = ((a+b)/2 × h) × d
Surface Area: SA = 2×((a+b)/2×h) + (a+b+2×√((b-a)²/4+h²))×d
where a and b are parallel bases, h is trapezoid height, d is prism depth
A trapezoidal prism is a three-dimensional solid with two parallel trapezoidal bases and four rectangular faces connecting them. It's commonly found in architecture, construction (roof trusses, retaining walls), and engineering applications.
Volume = ((a+b)/2 × h) × d, where a and b are the parallel sides of the trapezoid, h is the trapezoid height, and d is the prism depth. First calculate the trapezoid area, then multiply by the depth.
A rectangular prism has rectangular bases (4 right angles), while a trapezoidal prism has trapezoidal bases (one pair of parallel sides). Rectangular prisms are simpler to calculate since the base is just length × width.
Calculate: 2 × (trapezoid area) + (perimeter of trapezoid × depth). The trapezoid area is (a+b)/2 × h. Add this to the sum of all four rectangular side areas.
Use consistent units for all measurements. If using meters, volume will be in cubic meters (m³) and surface area in square meters (m²). Common units include cm, inches, feet, or meters.
Yes, a right trapezoid (with two right angles) can be the base of a trapezoidal prism. The volume formula remains the same, but surface area calculation may be simpler since some sides are perpendicular.
Trapezoidal prisms are common in roof trusses, drainage channels, retaining walls, and architectural elements. Their shape provides structural strength while allowing for drainage or aesthetic design features.
By definition, a trapezoid must have exactly one pair of parallel sides. If no sides are parallel, it's not a trapezoid but a general quadrilateral, and you'd need different formulas to calculate the prism's properties.