Lateral Area of a Trapezoidal Prism Calculator
Find the lateral surface area of a trapezoidal prism by entering the four sides of its trapezoidal cross-section and the height of the prism. The total surface area (including the two trapezoidal bases) is also shown when it can be computed.
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LA = (a + b + c + d) × H — sum of the four rectangular lateral faces
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Perimeter of trapezoid
a + b + c + d = 6 + 10 + 5 + 5 = 26 - 2
Lateral area
perimeter × H = 26 × 8 = 208Each of the four rectangular lateral faces contributes one side × H.
How does this calculator work?
Lateral area of a trapezoidal prism = (a + b + c + d) × H, where a and b are the parallel sides, c and d are the legs, and H is the prism height. Enter all five values to also get the trapezoid height, base area and total surface area.
Formula
How this is calculated
A trapezoidal prism is a solid with two congruent trapezoidal bases joined by four rectangular lateral faces. The lateral surface area counts only those rectangular faces. Each rectangle has one dimension equal to a side of the trapezoid (top base a, bottom base b, left leg c, or right leg d) and the other equal to the prism height H — the perpendicular distance between the two trapezoidal bases. Summing all four rectangles gives LA = (a + b + c + d) × H, which equals the trapezoid perimeter times H.
When the four trapezoid sides are geometrically consistent — meaning the legs and parallel sides can actually form a closed trapezoid — the calculator also derives the perpendicular height of the trapezoid using the two-equation system that comes from placing the trapezoid in a coordinate frame. The base area is then ½ × (a + b) × h_trap, and the total surface area is the lateral area plus twice the base area.
Assumptions: all inputs are positive lengths in the same unit. The four sides must form a valid trapezoid (the geometry is checked internally, and total SA is omitted if they cannot); a and b are the two parallel sides. The prism height H is the edge perpendicular to the trapezoidal bases, not the slant height.
Frequently asked questions
a is the top (shorter) parallel side and b is the bottom (longer) parallel side. c and d are the non-parallel legs connecting the two parallel sides. If the trapezoid is isosceles, c and d are equal.
The total surface area requires the perpendicular height of the trapezoidal face, which is derived from the four sides. If the given sides cannot form a real trapezoid (the legs are too short for the width difference between the bases), the height cannot be computed.
Lateral surface area includes only the four rectangular faces connecting the two trapezoidal bases. Total surface area adds both trapezoidal bases: TSA = LA + 2 × base area.
Also known as
TG we-Calculate Editorial Team. (2026). Lateral Area of a Trapezoidal Prism Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lateral-area-trapezoidal-prism-calculator
TG we-Calculate Editorial Team. "Lateral Area of a Trapezoidal Prism Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/lateral-area-trapezoidal-prism-calculator.
TG we-Calculate Editorial Team, "Lateral Area of a Trapezoidal Prism Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lateral-area-trapezoidal-prism-calculator
@misc{wecalculate_lateral_area_trapezoidal_prism_calculator, title = {Lateral Area of a Trapezoidal Prism Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lateral-area-trapezoidal-prism-calculator}}, year = {2026}, note = {TG we-Calculate} }
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