Total Surface Area of Elongated Pentagonal Bipyramid Given Height Calculator

Formula Used:

\[ TSA = \left(\frac{5\sqrt{3}}{2} + 5\right) \times \left(\frac{h}{\left(2\sqrt{\frac{5-\sqrt{5}}{10}}\right) + 1}\right)^2 \]

Total Surface Area (TSA):

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1. What is the Elongated Pentagonal Bipyramid?

The Elongated Pentagonal Bipyramid is a polyhedron formed by adding two pentagonal pyramids to a pentagonal prism. It has 12 faces (10 equilateral triangles and 2 pentagons), 20 edges, and 12 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \left(\frac{5\sqrt{3}}{2} + 5\right) \times \left(\frac{h}{\left(2\sqrt{\frac{5-\sqrt{5}}{10}}\right) + 1}\right)^2 \]

Where:

\( TSA \) — Total Surface Area (m²)
\( h \) — Height of the Elongated Pentagonal Bipyramid (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the total surface area based on the height of the elongated pentagonal bipyramid, incorporating geometric relationships between the height and surface dimensions.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important for various applications including material estimation, structural analysis, and geometric modeling of this specific polyhedral shape.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What are the main components of an elongated pentagonal bipyramid?
A: It consists of a central pentagonal prism with two pentagonal pyramids attached to its opposite pentagonal faces.

Q2: How many faces does this polyhedron have?
A: The elongated pentagonal bipyramid has 12 faces: 10 triangular faces and 2 pentagonal faces.

Q3: What is the symmetry of this shape?
A: It has D5h symmetry (dihedral pentagonal symmetry) when properly aligned.

Q4: Are there practical applications for this shape?
A: While primarily a mathematical construct, similar shapes appear in crystallography, architecture, and molecular structures.

Q5: How accurate is this formula?
A: The formula provides exact mathematical calculation for the total surface area based on the given height measurement.