Width of Elongated Dodecahedron given Total Surface Area Calculator

Formula Used:

\[ w = 3 \times \sqrt{\frac{TSA}{2 \times \sqrt{3} \times (3 + \sqrt{5})}} \]

Width of Elongated Dodecahedron (w):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Width of Elongated Dodecahedron?

The width of an elongated dodecahedron is the horizontal distance from the left most edge to the right most edge of this polyhedron. It's an important geometric measurement that helps define the spatial dimensions of this three-dimensional shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ w = 3 \times \sqrt{\frac{TSA}{2 \times \sqrt{3} \times (3 + \sqrt{5})}} \]

Where:

\( w \) — Width of elongated dodecahedron (m)
\( TSA \) — Total surface area of elongated dodecahedron (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula derives from the geometric properties of elongated dodecahedrons, relating the total surface area to the width measurement through mathematical constants and operations.

3. Importance of Width Calculation

Details: Calculating the width of an elongated dodecahedron is crucial for various applications including architectural design, 3D modeling, geometric analysis, and understanding the spatial properties of this specific polyhedral shape.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding width of the elongated dodecahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron formed by elongating a regular dodecahedron along one of its axes, resulting in a shape with 12 pentagonal faces and additional rectangular faces.

Q2: Why is the formula so complex?
A: The formula involves mathematical constants and operations that accurately represent the geometric relationship between surface area and width in this specific polyhedral shape.

Q3: What units should I use?
A: Use consistent units (typically meters for length and square meters for area). The calculator will return the width in the same length unit as the area unit's square root.

Q4: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to elongated dodecahedrons. Other polyhedrons have different geometric relationships between their dimensions and surface areas.

Q5: What if I get an error or unexpected result?
A: Ensure you've entered a valid positive number for the total surface area. Very small or very large values might be affected by computational precision limitations.