1. What is the 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 joined at their bases, resulting in 10 triangular faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area (m²)
• \( le \) — Edge Length (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula calculates the combined area of all 10 equilateral triangular faces of the pentagonal bipyramid.

3. Importance of Surface Area Calculation

Details: Calculating surface area is important in geometry, material science, and engineering applications where surface coverage, coating requirements, or heat transfer properties need to be determined.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and greater than zero for accurate calculation.

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 and 7 vertices.

Q2: Why is the formula multiplied by 5√3/2?
A: This comes from the area formula for equilateral triangles (√3/4 × side²) multiplied by 10 faces, simplified to 5√3/2 × side².

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.

Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, molecular geometry, architecture, and any field dealing with polyhedral structures.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect pentagonal bipyramid with equilateral triangular faces.