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Square Pyramid Surface, Slants and Positive Inverse Roots

Square Pyramid Surface, Slants and Positive Inverse Roots. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

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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, Pyramid height (H) 4 gives Base diagonal 8.4852814, Base surface area (A_b) 36, Lateral edge (d) 5.8309519, Slant height (s) 5, Lateral face area 15, Lateral surface area (A_l) 60, Volume (V) 48, Total surface area (A) 96.

V = a²H/3; s² = H²+a²/4; A = a²+2as

Worked example

Enter these known values and leave the other values blank.

Base length (a)
6 cm
Pyramid height (H)
4 cm
Base diagonal
8.4853 cm
Base surface area (A_b)
36 cm²
Lateral edge (d)
5.831 cm
Slant height (s)
5 cm
Lateral face area
15 cm²
Lateral surface area (A_l)
60 cm²
Volume (V)
48 cm³
Total surface area (A)
96 cm²

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. Retained inverse expressions select positive physical dimensions and use strict nondegenerate limits.
  • 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

Does square pyramid total surface include the base?

Yes. The square base area a² is added to the four triangular faces, whose combined area is 2as.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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