How this calculator works
A right regular hexagonal pyramid has six congruent triangular faces. Each has base a and face altitude s, so the lateral sheet is six copies of as/2. The closed total adds the regular hexagon. The piece table counts the six faces individually before adding the base. Perimeter or base-area inputs first recover a. A known lateral or total area can instead recover the slant and then vertical height. This models geometric surface area without seams, overlap or cutting waste.
Formula
P=6a; base B=3√3a²/2; apothem r=√3a/2; s=sqrt(h²+r²); face F=as/2; lateral L=6F=Ps/2; closed total S=B+L. Reverse: s=L/(3a) or (S-B)/(3a), then h=sqrt(s²-r²).
Worked example
An edge of 2 m and a vertical height of 1 m give slant 2 m. Six faces of 2 m² give lateral area 12 m². Adding the base, 6√3 m², gives total area about 22.39230485 m².
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Frequently asked questions
Which result should I use for a roof?
The lateral result measures the six sloping faces without the hexagonal base. Practical ordering also needs the appropriate overlap and waste allowances.
Can I use perimeter instead of edge length?
Yes. Divide the perimeter into six equal edges using the perimeter input. An irregular six-sided base does not satisfy these formulas.
Why can a total area be too small?
After removing the base, the remaining faces must have a slant longer than the base apothem. Otherwise the implied vertical height is zero or not real.