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Trapezoidal Prism Side-Wall and Closed Surface Areas

Trapezoidal Prism Side-Wall and Closed Surface Areas. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Trapezoid leg a 4, Parallel base b 8, Trapezoid leg c 5, Parallel base d 5, Cross-section perpendicular height 4, Prism depth 3 gives Lateral area 66, Surface area 118.

Lateral = depth(a+b+c+d); Total = Lateral+h(b+d)

Worked example

Enter these known values and leave the other values blank.

Trapezoid leg a
4 m
Parallel base b
8 m
Trapezoid leg c
5 m
Parallel base d
5 m
Cross-section perpendicular height
4 m
Prism depth
3 m
Lateral area
66 m²
Surface area
118 m²

Assumptions and limitations

  • The parallel bases are b and d; a and c are the legs. Cross-section height h is perpendicular between the bases, and prism depth is a separate measurement. The supplied legs, bases and height must describe one compatible trapezoid. Total area includes both trapezoidal ends.
  • Select compatible units and enough independent dimensions. Clear unknown values before solving backward. Numeric precision and display rounding do not quantify uncertainty in measured inputs.
  • Arithmetic uses 64 significant digits. Original reference diagrams explain the dimensions and do not follow entered proportions.
  • Geometric consistency uses a relative tolerance of 1e−12 to accommodate arithmetic rounding; it is not a measurement-error estimate.

Common questions

Do prism depth and trapezoid height mean the same thing?

No. Depth multiplies the cross-section perimeter to produce lateral area. Trapezoid height multiplies the sum of the parallel bases to produce both end areas.

References

Require physical dimensions and real positive inverse geometry; distinguish dependent measurements and cross-section consistency.

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