Volume of a Hexagonal Pyramid Calculator
Calculate the volume and surface area of a hexagonal pyramid using various input methods
Calculate Hexagonal Pyramid Volume
Length of one side of the hexagonal base
Perpendicular distance from base to apex
Calculation Results
Formula Used
Main Formula: V = (√3/2) × a² × h
Where: a = 0.0000 cm, h = 0 cm
Calculation: V = (√3/2) × (0.0000)² × 0 = 0.0000 cm³
Example Calculation
Problem
Find the volume of a regular hexagonal pyramid with a base perimeter of 12 cm and a height of 15 cm.
Solution
Given: Base perimeter (P) = 12 cm, Height (h) = 15 cm
Step 1: Find base edge: a = P/6 = 12/6 = 2 cm
Step 2: Apply formula: V = (√3/2) × a² × h
Step 3: V = (√3/2) × (2)² × 15 = (√3/2) × 4 × 15 = 30√3 ≈ 51.96 cm³
Answer: Volume = 51.96 cm³
Hexagonal Pyramid Properties
Base: Regular hexagon with 6 equal sides
Faces: 1 hexagonal base + 6 triangular faces = 7 faces total
Edges: 12 edges (6 base + 6 lateral)
Vertices: 7 vertices (6 base + 1 apex)
Apothem: Distance from center to edge midpoint
Key Formulas
Volume:
V = (√3/2) × a² × h
V = (2/√3) × ap² × h
V = (1/3) × BaseArea × h
Base Area:
A = (3√3/2) × a²
Apothem:
ap = (a√3)/2
Slant Height:
l = √(h² + ap²)
Quick Tips
All sides of the hexagonal base are equal in a regular pyramid
Height is perpendicular distance from base to apex
Apothem is always shorter than the base edge
Slant height is always longer than the height
Understanding Hexagonal Pyramids
What is a Hexagonal Pyramid?
A hexagonal pyramid is a three-dimensional geometric shape with a hexagonal (6-sided) base and six triangular faces that meet at a common point called the apex or vertex. When the base is a regular hexagon and the apex is directly above the center, it's called a regular hexagonal pyramid.
Key Components
- •Base Edge (a): Length of one side of the hexagonal base
- •Height (h): Perpendicular distance from base to apex
- •Apothem (ap): Distance from center to midpoint of any base edge
- •Slant Height (l): Distance from apex to midpoint of base edge
Volume Formula Derivation
The volume formula V = (√3/2) × a² × h comes from the general pyramid volume formula:
V = (1/3) × Base Area × Height
For a regular hexagon with side length a:
Base Area = (3√3/2) × a²
Therefore: V = (1/3) × (3√3/2) × a² × h = (√3/2) × a² × h
Alternative Formulas
Using apothem: V = (2/√3) × ap² × h ≈ 1.1547 × ap² × h
Using base area: V = (1/3) × BaseArea × h
General pyramid formula: V = (n/12) × h × a² × cot(π/n), where n = 6