1. What is the Height of Gyroelongated Pentagonal Pyramid?

The Height of Gyroelongated Pentagonal Pyramid is the vertical distance from the highest point to the lowest point of this complex polyhedron. It represents the maximum dimension of this Johnson solid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of the pyramid (m²)
• \( \sqrt{} \) — Square root function

Explanation: The formula combines geometric constants specific to pentagonal pyramids with the surface area to determine the vertical height.

3. Importance of Height Calculation

Details: Calculating the height is essential for understanding the spatial dimensions of this complex polyhedron, which has applications in architecture, crystallography, and mathematical modeling.

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 a Gyroelongated Pentagonal Pyramid?
A: It's a Johnson solid (J11) created by attaching a pentagonal antiprism to the base of a pentagonal pyramid.

Q2: Why is the formula so complex?
A: The complexity arises from the irregular geometry of pentagonal pyramids and the gyroelongation process that creates this specific polyhedron.

Q3: What are typical height values for this shape?
A: The height depends on the surface area, but typically ranges from a few centimeters to several meters in practical applications.

Q4: Can this formula be used for other pyramid types?
A: No, this formula is specific to gyroelongated pentagonal pyramids due to their unique geometric properties.

Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places, which is sufficient for most architectural and mathematical applications.