Hexagonal Pyramid Calculator

A regular hexagonal pyramid sits on a regular hexagonal base and tapers to a point (apex) directly above the center of the base. Six triangular faces connect the base to the apex.

The base area is the same as any regular hexagon: A = (3√3/2) × a². With base area and height, volume follows from the standard pyramid formula — one-third of base times height:

Volume = (1/3) × (3√3/2) × a² × h = (√3/2) × a² × h

The slant height l is the distance from the apex down to the midpoint of any base edge. That midpoint is the apothem away from the center, so:

Apothem = a × √3 / 2 Slant height l = √(h² + apothem²) = √(h² + 3a²/4)

Each triangular face has base a and height l (the slant height), giving 6 × (1/2 × a × l) = 3al for lateral surface area.

Lateral SA = 3al Total SA = 3al + (3√3/2) × a²

Worth noting: the slant height runs to the middle of the base edge, not to a corner. The edge from apex to corner is longer — it’s √(h² + a²). Some textbooks confuse these two, which leads to wrong surface area answers.

Hexagonal pyramids appear in architecture (some temple spires and decorative finials), in crystallography (some crystal forms have hexagonal pyramid symmetry), and in geometry textbooks as the classic six-sided variant of the general pyramid family.