Hexagonal Prism Calculator
Hexagonal Prism Volume and Surface Area Calculator
Calculate the volume and surface area of a hexagonal prism with our easy-to-use calculator. Learn about hexagonal prism formulas and explore interactive examples.
A hexagonal prism is a three-dimensional shape with two parallel hexagonal faces (bases) and six rectangular faces. It's a common shape in nature, architecture, and engineering, known for its efficiency and structural stability.
Formula
Volume = (3√3/2)a²h
Surface Area = 6ah + 3√3a²
Where:
- a:length of one side of the hexagonal base
- h:height of the prism (distance between bases)
How to Calculate Hexagonal Prism Volume
The volume is calculated by multiplying the area of the hexagonal base by the height. The base area formula uses the side length and involves the square root of 3 due to the hexagon's geometry.
Understanding Surface Area
The total surface area consists of two regular hexagonal bases and six rectangular faces. The base area uses the side length and √3, while the lateral area is the perimeter times height.
Real-World Applications
Hexagonal prisms appear in beehive cells, pencils, nuts and bolts, and architectural elements. Their efficient packing and structural strength make them ideal for many applications.
Frequently Asked Questions
What makes a hexagonal prism regular?
A regular hexagonal prism has bases that are regular hexagons (all sides equal, all angles 120°) and rectangular faces that are perpendicular to the bases.
Why are hexagonal prisms common in nature?
Hexagonal prisms are efficient shapes for packing and structural stability. Honeycomb cells are hexagonal prisms because this shape maximizes storage space while minimizing building material.
Where are hexagonal prisms used in engineering?
Hexagonal prisms are used in nuts and bolts, pencils, building columns, and various structural elements. They provide good strength-to-weight ratio and efficient space utilization.