Total Surface Area of Elongated Dodecahedron Calculator

Total Surface Area of Elongated Dodecahedron Formula:

\[ TSA = 2 \times \sqrt{3} \times (3 + \sqrt{5}) \times le^2 \]

Total Surface Area of Elongated Dodecahedron:

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

The Total Surface Area of an Elongated Dodecahedron is the total quantity of plane enclosed on the entire surface of the three-dimensional geometric shape known as the Elongated Dodecahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times \sqrt{3} \times (3 + \sqrt{5}) \times le^2 \]

Where:

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

Explanation: The formula calculates the total surface area by multiplying the square of the edge length by the constant factor \( 2 \times \sqrt{3} \times (3 + \sqrt{5}) \).

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is important in various fields including geometry, architecture, and material science where surface coverage, material requirements, or heat transfer properties need to be determined.

4. Using the Calculator

Tips: Enter the edge length of the elongated dodecahedron in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is an Elongated Dodecahedron?
A: An elongated dodecahedron is a polyhedron with 12 faces that has been stretched along one axis, creating a longer shape while maintaining its dodecahedral characteristics.

Q2: What units should I use for the edge length?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as the result will be in square units of that measurement.

Q3: Can this formula be used for regular dodecahedrons?
A: No, this specific formula is designed for elongated dodecahedrons. Regular dodecahedrons have a different surface area formula.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the provided formula. The accuracy of the result depends on the precision of the input value.

Q5: What are practical applications of this calculation?
A: This calculation is useful in architectural design, 3D modeling, material estimation for construction, and various engineering applications where elongated dodecahedral shapes are used.