Regular Pentagonal Prism Calculator

Volume

0 m3

Surface Area

0 m2

Lateral Area

0 m2

Base Area

0 m2

Height

0 m

Side Length

0 m

Apothem

0 m

Perimeter

0 m

Diagonal Length

0 m

Pentagonal Prism Volume and Surface Area Calculator

Calculate the volume and surface area of a pentagonal prism with our easy-to-use calculator. Learn about pentagonal prism formulas and explore interactive examples.

A pentagonal prism is a three-dimensional shape with two parallel pentagonal faces (bases) and five rectangular faces. It's commonly found in architecture, packaging, and various engineering applications.

Formula

Volume = (5a²/4) × cot(36°) × h
Surface Area = 5ah + 5a²/2 × cot(36°)

Where:

  • a:length of one side of the pentagonal base
  • h:height of the prism (distance between bases)

How to Calculate Pentagonal Prism Volume

The volume is calculated by multiplying the area of the pentagonal base by the height of the prism. The base area formula involves the side length and the cotangent of 36 degrees.

Understanding Surface Area

The total surface area consists of two regular pentagonal bases and five rectangular faces. The base area uses the side length and cotangent of 36 degrees, while the lateral area is the perimeter times height.

Real-World Applications

Pentagonal prisms are used in architectural columns, packaging design, and structural elements. They combine aesthetic appeal with structural stability.

Frequently Asked Questions

What makes a pentagonal prism regular?

A regular pentagonal prism has bases that are regular pentagons (all sides equal, all angles equal) and rectangular faces that are perpendicular to the bases.

How is a pentagonal prism different from other prisms?

A pentagonal prism has five rectangular faces and two pentagonal bases, while other prisms have different numbers of faces based on their base shape (e.g., triangular prism has three rectangular faces).

Where are pentagonal prisms used?

Pentagonal prisms are used in architecture (columns, beams), packaging (containers, boxes), and engineering (structural elements, optical components).

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