Hexagonal Pyramid Surface Area Calculator
Calculate total surface area, lateral surface area, and base area of hexagonal pyramids
Calculate Hexagonal Pyramid Surface Area
Length of one side of the hexagonal base
Height from base to apex
Surface Area Results
Formulas Used:
Base Area: BA = (3√3/2) × a² = 2.598 × a²
Face Area: FA = (1/2) × a × l
Lateral Surface Area: LSA = 6 × FA = 3al
Total Surface Area: SA = BA + LSA
Slant Height: l = √(h² + apothem²), where apothem = a√3/2
Alternative Formula: SA = (3√3/2)a² + 3a√(h² + 3a²/4)
Example Calculation
Example: Roof Design
Problem: Calculate surface area of a hexagonal pyramid roof with base edge 5 cm and height 5 cm
Given: Base length (a) = 5 cm, Height (h) = 5 cm
Solution
Apothem = 5 × √3/2 = 4.33 cm
Base Area = (3√3/2) × 5² = 64.95 cm²
Slant Height = √(5² + 4.33²) = √(25 + 18.75) = 6.61 cm
Face Area = (1/2) × 5 × 6.61 = 16.54 cm²
Lateral Surface Area = 6 × 16.54 = 99.22 cm²
Total Surface Area = 64.95 + 99.22 = 164.17 cm²
Surface Area Components
Base Area
Area of the hexagonal base
BA = 2.598 × a²
Lateral Surface Area
Sum of 6 triangular faces
LSA = 6 × face area
Face Area
Area of one triangular face
FA = (1/2) × a × l
Total Surface Area
Base + Lateral areas
SA = BA + LSA
Surface Area Tips
Base area is 2.598 times the square of edge length
Slant height forms the height of triangular faces
Six identical triangular faces form lateral surface
Can calculate using height or slant height
Understanding Hexagonal Pyramid Surface Area
What is Surface Area?
The surface area of a hexagonal pyramid is the total area of all its faces. It consists of the hexagonal base and six triangular faces. Understanding surface area is crucial for applications like material estimation, coating calculations, and geometric analysis.
Components Breakdown
- •Base Area: Area of the hexagonal foundation
- •Lateral Surface Area: Combined area of 6 triangular faces
- •Face Area: Area of individual triangular face
Key Surface Area Formulas
Base Area: BA = (3√3/2) × a² ≈ 2.598a²
Face Area: FA = (1/2) × a × l
Lateral Surface: LSA = 6 × FA = 3al
Total Surface: SA = BA + LSA
Alternative: SA = (3√3/2)a² + 3a√(h² + 3a²/4)
Real-World Applications
- • Architecture and roof design
- • Material estimation for construction
- • Packaging and container design
- • Paint and coating calculations
- • Geometric modeling and 3D printing