Hexagonal Pyramid
Calculate hexagonal pyramid volume, surface area, base area, lateral area, face area, and slant height from base length and height. Free online 3D geometry calculator with formula V = (sqrt3/2)a^2h and area breakdown chart.
About This Calculator
This Hexagonal Pyramid Calculator computes all key properties of a regular right hexagonal pyramid: volume, base area, lateral surface area, total surface area, face area, and slant height. Enter the base side length and vertical height to get instant results with a visual area comparison chart.
The calculator uses the following formulas for a regular hexagonal pyramid with base side a and height h:
- Volume: V = (sqrt3/2) x a^2 x h
- Base area: Ab = (3sqrt3/2) x a^2
- Slant height: l = sqrt(h^2 + 3a^2/4)
- Face area: Af = (a/2) x l
- Lateral surface area: Al = 6 x Af = 3a x l
- Total surface area: A = Ab + Al
A hexagonal pyramid has 7 faces (1 hexagonal base and 6 triangular faces), 7 vertices, and 12 edges. The hexagonal base can be divided into six equilateral triangles, each with side length equal to the base edge. The triangular lateral faces are isosceles triangles for a right regular pyramid.
The area breakdown chart visualizes the base area versus lateral area, helping you understand how the surface area is distributed between the base and the triangular faces. The composition chart shows the proportional split between base and lateral components of the total surface area.
Frequently Asked Questions
What is the formula for hexagonal pyramid volume?
The formula for the volume of a regular hexagonal pyramid is V = (sqrt3/2)a^2h, where a is the base side length and h is the vertical height. This comes from V = (1/3) x base area x height, where the base area of a regular hexagon is (3sqrt3/2)a^2.
How do you calculate 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 side length. Lateral area = 6 x face area where each triangular face area = (a/2) x sqrt(h^2 + 3a^2/4). The slant height l = sqrt(h^2 + 3a^2/4).
What is a hexagonal pyramid?
A hexagonal pyramid is a 3D geometric shape with a hexagonal base and an apex vertex connected to all six base vertices by triangular faces. It has 7 faces (1 hexagon + 6 triangles), 7 vertices, and 12 edges. When the apex is directly above the center of the hexagonal base, it is called a right regular hexagonal pyramid.
How many faces does a hexagonal pyramid have?
A hexagonal pyramid has 7 faces: one hexagonal base and six triangular lateral faces. Each triangular face connects one edge of the hexagonal base to the apex. This follows Euler's formula for polyhedra: V - E + F = 2, where V = 7 vertices, E = 12 edges, and F = 7 faces.
What is the slant height of a hexagonal pyramid?
The slant height of a hexagonal pyramid is the height of each triangular face from the base edge to the apex. It is calculated using the Pythagorean theorem: l = sqrt(h^2 + r^2), where h is the vertical height and r is the apothem of the hexagon. For a regular hexagon, apothem = (sqrt3/2)a, so l = sqrt(h^2 + 3a^2/4).
What is the base area of a regular hexagon?
The area of a regular hexagon with side length a is A = (3sqrt3/2)a^2. This can be derived by dividing the hexagon into six equilateral triangles, each with area (sqrt3/4)a^2, then multiplying by 6: 6 x (sqrt3/4)a^2 = (3sqrt3/2)a^2.
Is this hexagonal pyramid 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.