Total Surface Area of Triakis Tetrahedron given Height Calculator

Formula Used:

\[ TSA = \frac{5}{18} \times \sqrt{11} \times h^2 \]

Total Surface Area of Triakis Tetrahedron:

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1. What is Total Surface Area of Triakis Tetrahedron?

The Total Surface Area of a Triakis Tetrahedron is the total area of all the faces of the polyhedron. A Triakis Tetrahedron is a Catalan solid that can be formed by attaching a triangular pyramid to each face of a regular tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{5}{18} \times \sqrt{11} \times h^2 \]

Where:

\( TSA \) — Total Surface Area of Triakis Tetrahedron (m²)
\( h \) — Height of Triakis Tetrahedron (m)
\( \sqrt{11} \) — Square root of 11 (approximately 3.3166)

Explanation: This formula calculates the total surface area based on the height measurement of the Triakis Tetrahedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is important in various fields including architecture, engineering, material science, and 3D modeling. It helps in determining material requirements, heat transfer calculations, and structural analysis.

4. Using the Calculator

Tips: Enter the height of the Triakis Tetrahedron in meters. The height must be a positive value greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that results from attaching a triangular pyramid to each face of a regular tetrahedron. It has 12 faces, 18 edges, and 8 vertices.

Q2: Why is the formula specifically (5/18)*√11*h²?
A: This formula is derived from the geometric properties of the Triakis Tetrahedron and represents the mathematical relationship between its height and total surface area.

Q3: Can this calculator be used for other polyhedrons?
A: No, this calculator is specifically designed for Triakis Tetrahedrons. Other polyhedrons have different formulas for calculating surface area.

Q4: What units should I use for the height?
A: The calculator expects the height in meters, and the result will be in square meters. You can convert from other units as needed.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the formula. The result is rounded to 6 decimal places for practical use.