Trapezoidal Prism Surface Area Calculator

Yes. The calculator derives the slant leg length from the height and the difference between the two parallel bases, assuming both legs are equal. For isosceles: leg = sqrt(h^2 + ((a-b)/2)^2). This is accurate for symmetric shapes like gutters and channels.

A trapezoidal prism has 6 faces: 2 trapezoidal end faces (front and back), 1 top rectangle (shorter base x length), 1 bottom rectangle (longer base x length), and 2 slanted side rectangles (leg x length). The total surface area is the sum of all 6 face areas.

Lateral area includes only the 4 rectangular side faces (top, bottom, and two slanted sides) without the trapezoidal ends. Total surface area adds the 2 trapezoidal end faces to the lateral area. Use lateral area for wrapping calculations and total SA for material coverage.

This calculator assumes isosceles (equal legs). For a non-isosceles trapezoid, you need to know both leg lengths individually. Calculate each face area separately: 2 trapezoid ends + top rect + bottom rect + left side rect + right side rect.

Common applications include: calculating sheet metal for rain gutters, concrete formwork for retaining walls, lining material for irrigation channels, painting architectural columns, and cardboard for custom packaging boxes with trapezoidal cross-sections.

Volume uses the cross-sectional area times length: V = [(a+b)/2 x h] x L. Surface area adds all 6 faces: SA = 2 x [(a+b)/2 x h] + (a + b + 2 x leg) x L. For a prism with a=8, b=4, h=3, L=10: Volume = 6 x 3 x 10 = 180 cubic units. Surface area = 36 + 192.11 = 228.11 square units.

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