Height of Tetragonal Trapezohedron given Total Surface Area Calculator

Formula Used:

\[ h = \sqrt{\frac{1}{2}(4+3\sqrt{2})} \times \sqrt{\frac{TSA}{2\sqrt{2+4\sqrt{2}}}} \]

Height of Tetragonal Trapezohedron:

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1. What is the Height of Tetragonal Trapezohedron?

The height of a Tetragonal Trapezohedron is the distance between the two peak vertices where the long edges join. It's a crucial measurement in understanding the three-dimensional geometry of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{\frac{1}{2}(4+3\sqrt{2})} \times \sqrt{\frac{TSA}{2\sqrt{2+4\sqrt{2}}}} \]

Where:

\( h \) — Height of Tetragonal Trapezohedron (m)
\( TSA \) — Total Surface Area (m²)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the height based on the total surface area, incorporating the geometric properties of the tetragonal trapezohedron.

3. Importance of Height Calculation

Details: Calculating the height is essential for understanding the complete geometry of the tetragonal trapezohedron, which has applications in crystallography, materials science, and geometric modeling.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetragonal Trapezohedron?
A: A tetragonal trapezohedron is a polyhedron with eight faces, each of which is a kite. It is the dual polyhedron of a square antiprism.

Q2: What units should I use for the calculation?
A: The calculator uses meters for length and square meters for area. Ensure consistent units for accurate results.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for tetragonal trapezohedra and won't work for other polyhedral shapes.

Q4: What is the range of valid input values?
A: The total surface area must be a positive number greater than zero. Extremely small values may result in computational precision issues.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the given formula, though computational precision may introduce very small errors in the decimal places.