Total Surface Area Of Stellated Octahedron Given Edge Length Of Peaks Calculator

Formula Used:

\[ TSA = \frac{3}{2} \times \sqrt{3} \times (2 \times l_{e(Peaks)})^2 \]

Total Surface Area (TSA):

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1. What is Total Surface Area of Stellated Octahedron?

The Total Surface Area of a Stellated Octahedron is the total quantity of plane enclosed on the entire surface of the Stellated Octahedron. It represents the sum of the areas of all its faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{3}{2} \times \sqrt{3} \times (2 \times l_{e(Peaks)})^2 \]

Where:

\( TSA \) — Total Surface Area of Stellated Octahedron (m²)
\( l_{e(Peaks)} \) — Edge Length of Peaks of Stellated Octahedron (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula calculates the total surface area based on the edge length of the tetrahedral peaks attached to the faces of the octahedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric shapes is fundamental in various fields including architecture, engineering, and material science. It helps in determining material requirements, heat transfer properties, and structural characteristics.

4. Using the Calculator

Tips: Enter the edge length of peaks in meters. The value must be positive and valid. The calculator will compute the total surface area using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Stellated Octahedron?
A: A stellated octahedron is a polyhedron formed by attaching tetrahedral pyramids to each face of a regular octahedron, creating a star-like shape.

Q2: Why is the square root of 3 used in the formula?
A: The square root of 3 appears in many geometric calculations involving equilateral triangles and tetrahedra, which are fundamental components of the stellated octahedron.

Q3: What are the units of measurement?
A: The edge length should be provided in meters, and the resulting surface area will be in square meters (m²).

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

Q5: Is this formula applicable to all stellated polyhedra?
A: No, this specific formula applies only to the stellated octahedron with tetrahedral peaks. Other stellated polyhedra have different surface area formulas.