Free · 3D geometry calculators 📦

Square Pyramid Base, Single Face and Closed Surface

Square Pyramid Base, Single Face and Closed Surface. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

Formula & worked example
Private in your browser
No signup

Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
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, Height (h) 4 gives Slant height (l) 5, Base perimeter (P) 24, Total surface area (SA) 96, Base area (BA) 36, Lateral surface area (LSA) 60, Face area (FA) 15.

B = a²; F = as/2; L = 4F; A = B+L

Worked example

Enter these known values and leave the other values blank.

Base edge (a): 6 cm
Height (h): 4 cm

Slant height (l): 5 cm
Base perimeter (P): 24 cm
Total surface area (SA): 96 cm²
Base area (BA): 36 cm²
Lateral surface area (LSA): 60 cm²
Face area (FA): 15 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.
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.
Area-based height inverses use the positive square-root branch. Negative heights are not physical pyramid dimensions.

Common questions

Is one triangular face area the same as lateral area?

No. Four congruent triangular faces form the lateral surface. Multiply one face area by four.

References

Require physical dimensions and real positive inverse geometry; distinguish dependent measurements and cross-section consistency. Replace captured negative square-root height inverses with the positive root required by nondegenerate pyramid geometry. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

Explore 3d geometry calculators 📦 or browse all math calculators.