Hexagonal Prism — Definition, Formula & Examples

A hexagonal prism is a 3D shape with two parallel, congruent hexagonal bases connected by six rectangular faces. Think of it as a hexagon stretched out into a solid figure.

A hexagonal prism is a polyhedron consisting of two parallel, congruent hexagonal bases and six lateral faces that are parallelograms. When the lateral edges are perpendicular to the bases, it is called a right hexagonal prism, and the lateral faces are rectangles.

Key Formula

V = B \cdot h = \frac{3\sqrt{3}}{2}\,s^2 \cdot h

Where:

$V$ = Volume of the prism
$B$ = Area of the regular hexagonal base
$s$ = Side length of the regular hexagon
$h$ = Height (distance between the two bases)

How It Works

A hexagonal prism has 8 faces (2 hexagons and 6 rectangles), 18 edges, and 12 vertices. To find its volume, multiply the area of one hexagonal base by the height (the perpendicular distance between the bases). For a regular hexagonal prism, the base is a regular hexagon, so you can use the regular hexagon area formula. The surface area equals the combined area of both hexagonal bases plus the total area of the six rectangular lateral faces.

Worked Example

Problem: Find the volume of a regular hexagonal prism with a side length of 4 cm and a height of 10 cm.

Find the base area: Use the regular hexagon area formula with s = 4 cm.

B = \frac{3\sqrt{3}}{2}(4)^2 = \frac{3\sqrt{3}}{2} \cdot 16 = 24\sqrt{3} \approx 41.57 \text{ cm}^2

Multiply by the height: The volume equals the base area times the height of 10 cm.

V = 24\sqrt{3} \cdot 10 = 240\sqrt{3} \approx 415.7 \text{ cm}^3

Answer: The volume is

240\sqrt{3} \approx 415.7

cm³.

Why It Matters

Hexagonal prisms appear in everyday objects like pencils, nuts and bolts, and honeycomb structures. Understanding this shape builds your ability to calculate volumes and surface areas for real-world engineering and design problems.

Common Mistakes

Mistake: Using the side length of the hexagon as the height of the prism.

Correction: The side length s belongs to the hexagonal base, while the height h is the perpendicular distance between the two bases. These are different measurements — keep them separate in your formulas.