Pentagonal Prism Calculator

How to Calculate Pentagonal Prism Dimensions

A regular pentagonal prism is a three-dimensional solid with two parallel regular pentagonal bases and five rectangular lateral sides. It is defined by the base edge length a and the prism height/length L.

Regular Pentagonal Prism Formulas

The formulas below assume a regular pentagon base:

• Base Area (A_b): Ab = 0.25 * √(25 + 10√5) * a² ≈ 1.720477 * a²
• Volume (V): V = Ab * L ≈ 1.720477 * a² * L
• Lateral Surface Area (S_lat): Slat = 5 * a * L
• Total Surface Area (S): S = 2 * Ab + Slat ≈ 3.440955 * a² + 5 * a * L
• Apothem (incircle radius): apothem ≈ 0.688191 * a

Step-by-Step Worked Example

Calculate the properties of a pentagonal column with a base edge of 2 m and a height of 5 m:

1. Base Area: 1.720477 * 2² = 1.720477 * 4 ≈ 6.8819 m²
2. Volume: 6.8819 * 5 ≈ 34.41 m³
3. Lateral Area: 5 * 2 * 5 = 50 m²
4. Total Surface Area: 2 * 6.8819 + 50 = 13.7638 + 50 ≈ 63.764 m²

Also check: Pentagon Calculator, Hexagonal Prism Calculator, Rectangular Prism Calculator, Triangular Prism Calculator, Volume Calculator, Surface Area Calculator.