Free · Algebra and geometric models

Area of Solid and Built-Up Cross-Sections

Calculate ten common cross-section areas by combining rectangles, circular regions or triangular dimensions.

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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.

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

Formula and method

For the worked inputs, Area (A) = 12.

Rectangle A=wh; circle A=πd²/4; equilateral triangle A=√3s²/4

Worked example

Enter these known values and leave the other values blank.

Cross section
1
Width (W)
3 m
Height (H)
4 m
Area (A)
12 m²

Assumptions and limitations

  • Dimensions are positive and describe a planar cross-section.
  • Hollow sections subtract their interior voids; flange and web rectangles must fit within their outer dimensions.

Common questions

What must I enter?

Choose the mode when available and enter its independent known quantities. Leave an unknown editable quantity empty to use a supported inverse.

How should I use the result?

Interpret the numbers within the stated mathematical assumptions. Available unit selectors convert quantities; display rounding does not replace the internal calculation.

References

Equilateral triangle area uses the exact √3/4 coefficient in place of the captured 0.4330 approximation. Positive inverses use the matching exact expression. Explicit real-model bounds validate dimensions, inverse branches and discrete controls omitted or approximated in this capture. The ten geometric cross-section diagrams are replaced by original textual dimension and dissection descriptions with identical variant conditions.

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