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Total Surface Area of Pentagonal Bipyramid given Height Calculator

Formula Used:

\[ TSA = \frac{5\sqrt{3}}{2} \times \left( \frac{h}{2\sqrt{\frac{5-\sqrt{5}}{10}}} \right)^2 \]

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1. What is Total Surface Area of Pentagonal Bipyramid?

The Total Surface Area of a Pentagonal Bipyramid is the total area of all its triangular faces. A pentagonal bipyramid consists of two pentagonal pyramids sharing a common base, resulting in 10 identical triangular faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{5\sqrt{3}}{2} \times \left( \frac{h}{2\sqrt{\frac{5-\sqrt{5}}{10}}} \right)^2 \]

Where:

Explanation: The formula calculates the surface area based on the height of the bipyramid, incorporating geometric relationships specific to pentagonal structures.

3. Importance of Surface Area Calculation

Details: Calculating surface area is essential in various applications including material estimation, structural design, heat transfer analysis, and architectural planning for polyhedral structures.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a pentagonal bipyramid?
A: A pentagonal bipyramid is a polyhedron formed by two pentagonal pyramids sharing a common pentagonal base, resulting in 10 triangular faces, 7 vertices, and 15 edges.

Q2: How is this different from a regular pentagonal pyramid?
A: A pentagonal bipyramid has two apex points (top and bottom) instead of one, creating a symmetrical structure with identical triangular faces on both halves.

Q3: What are practical applications of pentagonal bipyramids?
A: These structures appear in molecular geometry, crystallography, architectural design, and as geometric models in various engineering fields.

Q4: Can this formula be used for irregular pentagonal bipyramids?
A: No, this formula specifically applies to regular pentagonal bipyramids where all triangular faces are congruent and the base is a regular pentagon.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric shapes. Real-world applications may require adjustments for material thickness and construction tolerances.

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