Hexagonal Pyramid Surface Area
Calculate hexagonal pyramid total surface area from base length and height. Get base area, lateral area, face area, and slant height with formula breakdown.
About This Calculator
The Hexagonal Pyramid Surface Area Calculator computes the total surface area of a regular right hexagonal pyramid given its base edge length and vertical height. A hexagonal pyramid has a hexagon-shaped base and six isosceles triangular faces that meet at a single apex point.
The calculator uses the following formulas for a regular hexagonal pyramid with base side a and height h:
- Base Area (BA) = (3sqrt3/2)a^2 -- area of the regular hexagon base
- Slant Height (l) = sqrt(h^2 + 3a^2/4) -- height of each triangular face
- Face Area (FA) = (a/2) x l -- area of one triangular face
- Lateral Surface Area (LSA) = 6 x FA = 3asqrt(h^2 + 3a^2/4)
- Total Surface Area (SA) = BA + LSA = (3sqrt3/2)a^2 + 3asqrt(h^2 + 3a^2/4)
This calculator is ideal for students studying geometry, architects, engineers, and anyone who needs quick and accurate surface area measurements for hexagonal pyramid structures. The results include a breakdown of base area, lateral area, and total surface area, along with a visual comparison chart.
This calculator works with any unit of measurement -- simply enter your base length and height in consistent units, and all results will be in the corresponding square units for areas and linear units for slant height.
Frequently Asked Questions
What is the formula for the surface area of a hexagonal pyramid?
The total surface area of a regular hexagonal pyramid is SA = Base Area + Lateral Area. Base Area = (3sqrt3/2)a^2 where a is the side length. Lateral Area = 6 x Face Area, where each triangular face area = (a/2) x sqrt(h^2 + 3a^2/4), and h is the vertical height. Combined: SA = (3sqrt3/2)a^2 + 3asqrt(h^2 + 3a^2/4).
How do I find the lateral surface area of a hexagonal pyramid?
The lateral surface area of a regular hexagonal pyramid is LSA = 3asqrt(h^2 + 3a^2/4), where a is the base edge length and h is the vertical height. This equals the sum of the areas of all six triangular faces.
What is the base area of a hexagonal pyramid?
The base area of a regular hexagonal pyramid equals the area of a regular hexagon: BA = (3sqrt3/2)a^2, where a is the side length. This is approximately 2.598 times the square of the side length.
How do I calculate the slant height of a hexagonal pyramid?
The slant height of a regular hexagonal pyramid is l = sqrt(h^2 + 3a^2/4), where h is the vertical height and a is the base side length. This is derived from the Pythagorean theorem using the pyramid height and the apothem of the hexagonal base (which is (sqrt3/2)a).
How many faces does a hexagonal pyramid have?
A hexagonal pyramid has 7 faces: one hexagonal base and six isosceles triangular lateral faces. It has 7 vertices and 12 edges, satisfying Euler's formula V - E + F = 2.
What is the difference between a hexagonal pyramid and a hexagonal prism?
A hexagonal pyramid has a hexagonal base with six triangular faces meeting at a single apex point, giving 7 faces total. A hexagonal prism has two parallel hexagonal bases connected by six rectangular faces, giving 8 faces total. The pyramid tapers to a point while the prism maintains a constant cross-section.
Is this hexagonal pyramid surface area calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration required. You can also share your calculation results via URL for easy reference.