Total Surface Area of Elongated Dodecahedron given Height Calculator

Formula Used:

\[ TSA = 2 \times \sqrt{3} \times (3 + \sqrt{5}) \times \left(\frac{h}{\sqrt{3}}\right)^2 \]

Total Surface Area (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Total Surface Area of Elongated Dodecahedron?

The Total Surface Area of an Elongated Dodecahedron refers to the total quantity of plane enclosed on the entire surface of this polyhedron. It is an important geometric measurement used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times \sqrt{3} \times (3 + \sqrt{5}) \times \left(\frac{h}{\sqrt{3}}\right)^2 \]

Where:

\( TSA \) — Total Surface Area (m²)
\( h \) — Height of Elongated Dodecahedron (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{5} \) — Square root of 5 (approximately 2.236)

Explanation: This formula calculates the total surface area based on the height of the elongated dodecahedron, incorporating mathematical constants and geometric relationships.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, structural analysis, and geometric modeling in mathematics and engineering fields.

4. Using the Calculator

Tips: Enter the height of the elongated dodecahedron in meters. The value must be positive and valid. The calculator will compute the total surface area based on the provided height.

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, creating a shape with 12 regular pentagonal faces and additional rectangular faces.

Q2: Why is the formula so complex?
A: The formula incorporates mathematical constants and geometric relationships specific to the elongated dodecahedron's structure, ensuring accurate surface area calculations.

Q3: What units should I use for the height?
A: The height should be entered in meters (m), and the result will be in square meters (m²) for surface area.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for height with up to 4 decimal places precision.

Q5: Are there any limitations to this calculation?
A: This calculation assumes a perfect geometric elongated dodecahedron shape. For real-world applications, additional factors may need to be considered.