1. What is the Edge Length of Gyroelongated Square Pyramid?

The edge length of a gyroelongated square pyramid is the length of any edge of this geometric solid, which consists of a square pyramid attached to a square antiprism.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge length of gyroelongated square pyramid (m)
• \( SA_{Total} \) — Total surface area of the pyramid (m²)

Explanation: This formula calculates the edge length based on the total surface area of the gyroelongated square pyramid, using the mathematical relationship between surface area and edge length.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the dimensions and proportions of the gyroelongated square pyramid, which is important in geometric modeling, architectural design, and mathematical analysis of polyhedra.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid for accurate calculation of the edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a gyroelongated square pyramid?
A: A gyroelongated square pyramid is a Johnson solid formed by attaching a square pyramid to a square antiprism, creating a polyhedron with triangular and square faces.

Q2: Why is the formula structured this way?
A: The formula derives from the geometric relationship between the total surface area and the edge length in this specific polyhedron, incorporating the mathematical constant √3.

Q3: What are the units for edge length?
A: The edge length is measured in meters (m), consistent with the surface area input in square meters (m²).

Q4: Can this calculator handle different units?
A: The calculator uses consistent SI units. For other units, convert the surface area to square meters before calculation.

Q5: What is the precision of the calculation?
A: The calculator provides results rounded to 10 decimal places for accuracy while maintaining reasonable precision.