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Right Square Pyramid Heights, Faces and Volume

Right Square Pyramid Heights, Faces and Volume. 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 edge (a) 6, Pyramid height (H) 4 gives Slant height (s) 5, Lateral edge (d) 5.8309519, Base diagonal 8.4852814, Lateral face area (A_f) 15, Base area (A_b) 36, Total lateral area (A_l) 60, Total surface area (A) 96, Volume (V) 48.

V = a²H/3; s² = H²+a²/4; d² = H²+a²/2

Worked example

Enter these known values and leave the other values blank.

Base edge (a)
6 cm
Pyramid height (H)
4 cm
Slant height (s)
5 cm
Lateral edge (d)
5.831 cm
Base diagonal
8.485 cm
Lateral face area (A_f)
15 cm²
Base area (A_b)
36 cm²
Total lateral area (A_l)
60 cm²
Total surface area (A)
96 cm²
Volume (V)
48 cm³

Assumptions and limitations

  • The apex sits above the center of a square base. Perpendicular height H reaches the base center; slant height s reaches a base-edge midpoint; lateral edge d reaches a corner. Base area is one square and lateral area is the sum of four triangular faces.
  • 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.

Common questions

How is square pyramid volume related to a matching prism?

Its volume is one third of a prism with the same base area and perpendicular height.

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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