N Gon Prism Calculator

An n-gon prism is a three-dimensional geometric shape with two identical n-sided polygonal bases and rectangular faces connecting corresponding sides of the bases. This calculator helps you determine the volume and surface area of an n-gon prism based on the number of sides, side length, and height.

Introduction

An n-gon prism is a polyhedron with two parallel, congruent n-sided polygonal bases and rectangular lateral faces connecting corresponding sides of the bases. The term "n-gon" refers to any polygon with n sides, where n is an integer greater than or equal to 3.

This calculator provides a straightforward way to compute the volume and surface area of an n-gon prism. Understanding these properties is essential in various fields including architecture, engineering, and physics.

Formulas

Volume of an N-gon Prism

Volume = Base Area × Height Base Area = (n × s²) / (4 × tan(π/n))

Where:

n = number of sides of the base polygon
s = length of each side of the base polygon
h = height of the prism

Surface Area of an N-gon Prism

Surface Area = 2 × Base Area + Lateral Area Lateral Area = Perimeter × Height Perimeter = n × s

The surface area includes the area of the two bases and the lateral area formed by the rectangular faces.

How to Use the Calculator

Enter the number of sides (n) of the base polygon.
Enter the length of each side (s) of the base polygon.
Enter the height (h) of the prism.
Click the "Calculate" button to compute the volume and surface area.
Review the results and use the chart for visualization.

Note: The number of sides must be an integer greater than or equal to 3. Side length and height must be positive numbers.

Example Calculation

Let's calculate the volume and surface area of a pentagonal prism (n=5) with each side length of 4 units and height of 10 units.

Base Area = (5 × 4²) / (4 × tan(π/5)) ≈ 22.88 units² Volume = 22.88 × 10 = 228.8 cubic units Perimeter = 5 × 4 = 20 units Lateral Area = 20 × 10 = 200 units² Surface Area = 2 × 22.88 + 200 = 245.76 units²

This example demonstrates how the calculator computes the properties of an n-gon prism.

Frequently Asked Questions

What is an n-gon prism?: An n-gon prism is a three-dimensional shape with two identical n-sided polygonal bases and rectangular lateral faces connecting corresponding sides of the bases.
How do I calculate the volume of an n-gon prism?: Multiply the area of the base polygon by the height of the prism. The base area can be calculated using the formula (n × s²) / (4 × tan(π/n)).
What is the difference between volume and surface area?: Volume measures the amount of space inside the prism, while surface area measures the total area of all its faces.
Can I use this calculator for any n-gon?: Yes, the calculator works for any n-gon where n is an integer greater than or equal to 3.
What units should I use for the inputs?: You can use any consistent unit of measurement (e.g., meters, centimeters, inches) for the side length and height.