1. What Is The Gyroelongated Pentagonal Pyramid?

The Gyroelongated Pentagonal Pyramid is a Johnson solid constructed by attaching a pentagonal antiprism to the base of a pentagonal pyramid. It has 16 faces: 15 equilateral triangles and 1 regular pentagon.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area
• \( le \) — Edge Length
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.236)

Explanation: The formula combines the surface areas of all triangular and pentagonal faces of the polyhedron.

3. Importance of TSA Calculation

Details: Calculating the total surface area is essential for various applications including material estimation, structural analysis, and geometric modeling of this complex polyhedron.

4. Using The Calculator

Tips: Enter the edge length in meters. The value must be positive. The calculator will compute the total surface area in square meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Johnson solid?
A: Johnson solids are convex polyhedra with regular faces that are not uniform (unlike Platonic or Archimedean solids).

Q2: How many faces does a gyroelongated pentagonal pyramid have?
A: It has 16 faces: 15 equilateral triangles and 1 regular pentagon.

Q3: What are the real-world applications of this shape?
A: This geometric shape finds applications in architecture, molecular structures, and decorative art designs.

Q4: Can this formula be used for any edge length?
A: Yes, the formula works for any positive edge length, as it's a scaling relationship.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though practical measurements may have precision limitations.