Hexagonal Pyramid Calculator
Calculate volume, surface area, and all properties of a hexagonal pyramid
Calculate Hexagonal Pyramid Properties
Length of one side of the hexagonal base
Height from base to apex
Hexagonal Pyramid Properties
Formulas Used:
Base Area: Ab = (3√3/2) × a²
Volume: V = (√3/2) × a² × h
Slant Height: l = √(h² + (a√3/2)²)
Face Area: Af = (1/2) × a × l
Lateral Surface Area: Al = 6 × Af
Total Surface Area: Atotal = Ab + Al
Example Calculation
Example: Tent Design
Problem: Design a hexagonal pyramid tent with base edge 4 mm and height 5 mm
Given: Base length (a) = 4 mm, Height (h) = 5 mm
Solution
Base Area = (3√3/2) × 4² = 20.78 mm²
Volume = (√3/2) × 4² × 5 = 69.28 mm³
Slant Height = √(5² + (4√3/2)²) = √(25 + 12) = 6.08 mm
Face Area = (1/2) × 4 × 6.08 = 12.17 mm²
Total Surface Area = 20.78 + 6 × 12.17 = 93.8 mm²
Hexagonal Pyramid Properties
Hexagonal Base
Regular hexagon with 6 equal sides
Triangular Faces
6 isosceles triangular faces
Apex Vertex
Single point at the top
Total Edges
6 base edges + 6 lateral edges
Calculation Tips
Regular hexagon has 6 equal sides and angles
Slant height is the height of triangular faces
Volume formula uses base area × height ÷ 3
Total surface area = base + lateral areas
Understanding Hexagonal Pyramids
What is a Hexagonal Pyramid?
A hexagonal pyramid is a three-dimensional shape with a hexagonal base and six triangular faces that meet at a single point called the apex. It has 7 vertices (6 on the base + 1 apex), 12 edges (6 on the base + 6 lateral), and 7 faces (1 base + 6 triangular).
Real-World Applications
- •Architecture and building design
- •Tent and pavilion structures
- •Crystal formations in geology
- •Packaging and container design
Key Formulas
Base Area: Ab = (3√3/2) × a²
Volume: V = (√3/2) × a² × h
Slant Height: l = √(h² + apothem²)
Face Area: Af = (1/2) × a × l
Lateral Surface: Al = 6 × Af
Total Surface: Atotal = Ab + Al
Formula Variables
- a: Length of base edge
- h: Height of pyramid (base to apex)
- l: Slant height of triangular faces
- apothem: Distance from center to side = a√3/2