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Regular Hexagonal Pyramid Volume Calculator — result sheet
Calculate the base area, volume, perimeter, apothem, and slant height of a regular hexagonal pyramid from its side and vertical height.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Base area B = (3√3/2)s²; volume V = Bh/3; hexagon apothem a = √3s/2; slant height l = √(h²+a²).
This is a regular pyramid whose base is a regular hexagon and whose apex is centered over the base. The vertical height and slant height are different measurements, so the calculator derives both while keeping its main answer focused on the solid's volume.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Base side length — length units; minimum 1.0E-6; maximum 1000000000
- Vertical height — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Base side length | 4 |
| Vertical height | 9 |
Base area ≈41.5692 square units; volume ≈124.7077 cubic units; base perimeter =24; slant height ≈9.6437 length units.
Assumptions and limits
- The base is a regular hexagon with six equal sides.
- The apex is directly above the center of the base.
- Vertical height is perpendicular to the base plane and is positive.
- Slant height is measured from the apex to the midpoint of a base side.
- The pyramid is an ideal Euclidean solid with no wall thickness or material loss.
- Volume uses cubic length units; the base area and related dimensions retain their own units.
- Lateral and total surface areas are intentionally not modeled because a separate surface-area contract covers that question.
- The formula does not apply to an off-center apex or an irregular hexagonal base.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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