Long Edge Of Pentagonal Trapezohedron Given Total Surface Area Calculator

Formula Used:

\[ Long Edge = \frac{\sqrt{5} + 1}{2} \times \sqrt{\frac{Total Surface Area}{\sqrt{\frac{25}{2} \times (5 + \sqrt{5})}}} \]

Long Edge of Pentagonal Trapezohedron:

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1. What is Long Edge of Pentagonal Trapezohedron?

The Long Edge of Pentagonal Trapezohedron refers to the length of any of the longer edges of this specific polyhedron shape. A pentagonal trapezohedron is a polyhedron with ten faces, each being a kite shape, arranged in two pentagonal rings.

2. How Does the Calculator Work?

The calculator uses the following formula to calculate the long edge from total surface area:

\[ Long Edge = \frac{\sqrt{5} + 1}{2} \times \sqrt{\frac{Total Surface Area}{\sqrt{\frac{25}{2} \times (5 + \sqrt{5})}}} \]

3. Formula Explanation

Components of the formula:

\(\sqrt{5}\) — Square root of 5 (approximately 2.23607)
Total Surface Area — The total surface area of the pentagonal trapezohedron
The formula combines geometric constants specific to pentagonal symmetry

4. Using the Calculator

Instructions: Enter the total surface area of the pentagonal trapezohedron in square meters. The value must be greater than zero. Click "Calculate" to get the long edge length.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for input?
A: The calculator expects total surface area in square meters (m²) and returns the long edge in meters (m).

Q2: Can I use this calculator for other polyhedrons?
A: No, this formula is specific to pentagonal trapezohedrons only.

Q3: What is the precision of the calculation?
A: The result is rounded to 6 decimal places for practical use.

Q4: Are there any limitations to this formula?
A: The formula assumes a perfect pentagonal trapezohedron shape and may not be accurate for irregular shapes.

Q5: Can I calculate total surface area from long edge?
A: Yes, the formula can be rearranged to solve for total surface area given the long edge.