Hexagonal Pyramid Surface Area Calculator
Calculate the total surface area (base + six triangular faces) and lateral surface area of a regular hexagonal pyramid. Provide the base side length plus either the perpendicular height or the slant height.
Known dimensions
SA = Base area + Lateral area = (3√3/2)a² + 3al
Base area
Base apothem
Slant height
Lateral area
Total surface area
- 1
Base apothem
ap = (√3 ÷ 2) × 6 = 5.1962Perpendicular distance from the base centre to the midpoint of a base edge - 2
Slant height
l = √(10² + 5.1962²) = 11.2694 - 3
Base area
B = (3√3 ÷ 2) × 6² = 93.5307 - 4
Lateral area
LA = 3 × 6 × 11.2694 = 202.8497 - 5
Total surface area
SA = 93.5307 + 202.8497 = 296.3804
How does this calculator work?
Total surface area of a regular hexagonal pyramid = (3√3/2)a² + 3al, where a is the base side and l = √(h² + 3a²/4) is the slant height. Base area (3√3/2)a² plus six identical triangles each with area (1/2)al.
Formula
How this is calculated
The surface area of a hexagonal pyramid has two parts: the regular hexagonal base and the six congruent isosceles triangular faces that meet at the apex. The base area is (3√3/2)a², where a is the side length. The slant height l is the altitude of each triangular face — it runs from the apex perpendicular to the midpoint of the corresponding base edge. When the perpendicular height h is given, the slant height is derived using the Pythagorean theorem applied along the face: l = √(h² + ap²), where ap = (√3/2)a is the apothem of the hexagonal base.
The area of one triangular face is (1/2) × base × height = (1/2) × a × l. Because there are six identical faces, the lateral surface area is 3al. Adding the base area gives the total surface area SA = (3√3/2)a² + 3al.
If the slant height is already known (e.g. from a blueprint), select that input mode. The calculator also back-calculates the perpendicular height h = √(l² − ap²) when slant height is provided.
Frequently asked questions
The slant height l runs from the apex to the midpoint of a base edge (the altitude of a triangular face). The lateral edge e runs from the apex to a base vertex. For a regular hexagonal pyramid with side a and height h: l = √(h² + 3a²/4) and e = √(h² + a²). Both are longer than h.
Yes — these formulas apply only to a right regular hexagonal pyramid where the apex is directly above the centre of the base and all six triangular faces are congruent. An oblique pyramid has triangular faces of different sizes and requires computing each face area separately.
A hexagonal pyramid has 7 faces: one hexagonal base and six triangular lateral faces. It also has 12 edges (6 base edges + 6 lateral edges) and 7 vertices (6 base vertices + 1 apex).
Also known as
TG we-Calculate Editorial Team. (2026). Hexagonal Pyramid Surface Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hexagonal-pyramid-surface-area-calculator
TG we-Calculate Editorial Team. "Hexagonal Pyramid Surface Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/hexagonal-pyramid-surface-area-calculator.
TG we-Calculate Editorial Team, "Hexagonal Pyramid Surface Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hexagonal-pyramid-surface-area-calculator
@misc{wecalculate_hexagonal_pyramid_surface_area_calculator, title = {Hexagonal Pyramid Surface Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hexagonal-pyramid-surface-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?