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Regular Hexagonal Pyramid Face Areas and Capacity

Regular Hexagonal Pyramid Face Areas and Capacity. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • Formula & worked example
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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) 2, Pyramid height (h) 4 gives Base area 10.392305, Face area 4.3588989, Lateral surface area 26.153394, Total surface area 36.545699, Volume 13.856406.

B = 3√3 a²/2; s² = H²+3a²/4; L = 3as; V = BH/3

Worked example

Enter these known values and leave the other values blank.

Base length (a)
2 mm
Pyramid height (h)
4 mm
Face area
4.359 mm²
Base area
10.392 mm²
Lateral surface area
26.153 mm²
Total surface area
36.546 mm²
Volume
13.856 mm³

Assumptions and limitations

  • The base is a regular hexagon with six equal sides, and the apex lies above its center. The base apothem is a√3/2. Slant height reaches an edge midpoint, not a base vertex. Lateral area is the sum of six triangular face areas. Initial displayed units are millimeters, square millimeters and cubic millimeters.
  • 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 many triangular faces does a hexagonal pyramid have?

It has six lateral triangular faces plus one regular hexagonal base. Lateral area is six times one face area.

References

Require physical dimensions and real positive inverse geometry; distinguish dependent measurements and cross-section consistency.

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