Hexagonal Pyramid Calculator
Calculate volume, surface area, and other properties of a hexagonal pyramid
Calculation Results
Enter hexagonal pyramid measurements to calculate all properties.
Base Area (B): square units
Height (h): units
Volume (V): cubic units
Lateral Area (L): square units
Surface Area (A): square units
Base Perimeter (P): units
Slant Height (l): units
Apothem (ap): units
Hexagonal Pyramid Diagram
Hexagonal Pyramid Formulas
Key Properties
- Base Area (B): Area of the hexagonal base
- Height (h): Perpendicular distance from base to apex
- Volume (V): Space contained within the pyramid
- Lateral Area (L): Area of the six triangular faces
- Surface Area (A): Total area including the base
- Base Perimeter (P): Perimeter of the hexagonal base
- Slant Height (l): Height of the triangular faces
- Apothem (ap): Distance from center to midpoint of a base side
Calculation Formulas
- Base Area (Regular): B = (3√3/2) × a²
- Base Area (General): B = 3 × a × ap
- Volume (V): V = ⅓ × B × h
- Surface Area (A): A = B + L
- Base Perimeter (P): P = 6 × a
- Regular Hexagon Apothem: ap = (a√3)/2
- Slant Height (Regular): l = √(h² + ap²)
- Lateral Area (Regular): L = 3 × a × l
Where: a = base side length, h = height of pyramid, ap = apothem of base, l = slant height
Example Calculation
For a regular hexagonal pyramid with:
Edge length (a) = 5 units, Height (h) = 10 units.Calculations:
- Apothem ≈ (5 × √3)/2 ≈ 4.33 units
- Base Area ≈ (3√3/2) × 5² ≈ 64.95 units²
- Base Perimeter = 6 × 5 = 30 units
- Volume ≈ ⅓ × 64.95 × 10 ≈ 216.50 units³
- Slant Height ≈ √(10² + 4.33²) ≈ 10.90 units
- Lateral Area ≈ 3 × 5 × 10.90 ≈ 163.50 units²
- Surface Area ≈ 64.95 + 163.50 ≈ 228.45 units²
About Hexagonal Pyramids
A hexagonal pyramid is a three-dimensional shape with a hexagonal base and six triangular faces meeting at a common apex. It has 7 faces, 12 edges, and 7 vertices. When the base is a regular hexagon and the apex is directly above the center, it's called a regular hexagonal pyramid.
Real-World Applications
- Architecture: Some roof designs and tower structures
- Design: Geometric art and decorative elements
- Chemistry: Molecular structures with hexagonal symmetry
- Mathematics: Study of polyhedrons and geometry
Types of Hexagonal Pyramids
- Regular Hexagonal Pyramid: Base is a regular hexagon, apex directly above center
- Irregular Hexagonal Pyramid: Base is an irregular hexagon
- Right Hexagonal Pyramid: Apex is directly above the base's centroid
- Oblique Hexagonal Pyramid: Apex is not aligned with the base's centroid
Hexagonal Pyramid Components
Base Area (B)
B = 3 × a × ap
Pyramid Height (h)
Lateral Area (L)
L = 3 × a × l
Surface Area (A)
A = B + L
Base Perimeter (P)
P = 6 × a
Volume (V)
V = ⅓ × B × h
How to Use the Hexagonal Pyramid Calculator
The Hexagonal Pyramid Calculator helps compute various properties based on input values. Here's how to use it:
1. Select Calculation Method
Choose what measurements you know:
- Base Dimensions & Height - Enter base side length, apothem and pyramid height
- Base Area & Height - When you know the base area
- Volume & Base Area - To find the pyramid height
- Surface Area - When you know total surface area
- Regular Hexagon - When base is a regular hexagon
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Side length = 5, Apothem = 4.33, Height = 10
Example 2: Edge length = 5, Height = 10 (for regular hexagon)
3. Get Results
The calculator will compute all properties:
- Base Area (B)
- Pyramid Height (h)
- Volume (V)
- Lateral Area (L)
- Surface Area (A)
- Base Perimeter (P)
- Slant Height (l)
- Apothem (ap)
Practical Applications
- Calculate material needed for hexagonal pyramid structures
- Determine paint required for pyramid-shaped objects
- Find storage capacity of hexagonal pyramid containers
- Solve geometry problems involving hexagonal pyramids
Hexagonal Pyramid Formulas
| Parameter | Formula | Description |
|---|---|---|
| Base Side Length (a) | Given | Length of hexagon's side |
| Base Area (Regular) | (3√3/2) × a² | Area of regular hexagonal base |
| Base Area (General) | 3 × a × ap | Area using side length and apothem |
| Height (h) | Given or calculated | Height from apex to base |
| Volume (V) | (B × h)/3 | Volume of the pyramid |
| Apothem (Regular) | (a√3)/2 | Distance from center to side midpoint |
| Slant Height (Regular) | √(h² + ap²) | Height of triangular faces |
| Lateral Area (Regular) | 3 × a × l | Sum of areas of the 6 lateral faces |
| Surface Area (A) | B + L | Total surface area (base + lateral) |
| Base Perimeter (P) | 6 × a | Perimeter of the base |
Frequently Asked Questions
A hexagonal pyramid has a hexagonal base and triangular faces meeting at an apex, while a hexagonal prism has two hexagonal bases connected by rectangular faces.
A hexagonal pyramid has 7 faces - one hexagonal base and six triangular lateral faces.
Use the formula: l = √(h² + ap²) where h is height and ap is apothem.