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Right Rectangular Pyramid Capacity and Two Face Slants

Right Rectangular Pyramid Capacity and Two Face Slants. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • Formula & worked example
  • Private in your browser
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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: Base length (a) 6, Base width (b) 8, Pyramid height (H) 12 gives Base diagonal 10, Base surface area (A_b) 48, Lateral edge (d) 13, Slant of face with base length a 12.649111, Slant of face with base width b 12.369317, First lateral face area 37.947332, Second lateral face area 49.477268, Total surface area (A) 222.8492, Volume (V) 192.

V = abH/3; sa² = H²+(b/2)²; sb² = H²+(a/2)²

Worked example

Enter these known values and leave the other values blank.

Base length (a)
6 cm
Base width (b)
8 cm
Pyramid height (H)
12 cm
Total surface area (A)
222.85 cm²
Volume (V)
192 cm³

Assumptions and limitations

  • The apex is above the rectangular base center. Slant height for a face with base length a depends on the perpendicular base width b, and vice versa. Total surface includes the rectangular base and two faces of each kind.
  • 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.
  • The captured public workflow takes base length, base width and perpendicular height. Its additional face measures remain internal; they are not editable controls in this workflow.

Common questions

Why are the two slant heights different?

The distances from the base center to the two kinds of edges are half the opposite base dimensions. Unequal base dimensions therefore produce unequal face slants.

References

Require physical dimensions and real positive inverse geometry; distinguish dependent measurements and cross-section consistency. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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