Height of Elongated Pentagonal Bipyramid given Total Surface Area Calculator

Formula Used:

\[ Height = \left(2 \times \sqrt{\frac{5 - \sqrt{5}}{10}} + 1\right) \times \sqrt{\frac{Total\ Surface\ Area}{\frac{5 \times \sqrt{3}}{2} + 5}} \]

Height of Elongated Pentagonal Bipyramid:

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1. What is the Height of Elongated Pentagonal Bipyramid?

The height of an elongated pentagonal bipyramid is the vertical distance from the highest point to the lowest point of this geometric solid. It is an important measurement in geometry and 3D modeling.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Height = \left(2 \times \sqrt{\frac{5 - \sqrt{5}}{10}} + 1\right) \times \sqrt{\frac{Total\ Surface\ Area}{\frac{5 \times \sqrt{3}}{2} + 5}} \]

Where:

\( Total\ Surface\ Area \) — The total surface area of the elongated pentagonal bipyramid (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the height based on the total surface area, using geometric relationships specific to the elongated pentagonal bipyramid shape.

3. Importance of Height Calculation

Details: Calculating the height of geometric solids is essential for various applications including architectural design, 3D modeling, material estimation, and geometric analysis.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated pentagonal bipyramid?
A: An elongated pentagonal bipyramid is a polyhedron formed by elongating a pentagonal bipyramid by inserting a pentagonal prism between its two halves.

Q2: What are the units for the input and output?
A: The input (total surface area) should be in square meters, and the output (height) will be in meters.

Q3: Can this calculator handle different units?
A: No, the calculator is designed for square meters input and meters output. Convert other units to these before calculation.

Q4: What is the precision of the calculation?
A: The result is calculated with high precision and rounded to 6 decimal places for display.

Q5: Are there any limitations to this formula?
A: This formula is specifically designed for elongated pentagonal bipyramids and may not apply to other geometric shapes.