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Total Surface Area of Gyroelongated Square Pyramid Formula:
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The Total Surface Area (TSA) of a Gyroelongated Square Pyramid is the total area of all its faces. It is calculated using the formula that incorporates the edge length of the pyramid.
The calculator uses the formula:
Where:
Explanation: The formula accounts for the geometric properties of the gyroelongated square pyramid, combining the base area and the lateral surface areas.
Details: Calculating the total surface area is essential for applications in geometry, architecture, and material estimation, providing insight into the spatial extent of the pyramid.
Tips: Enter the edge length in meters. The value must be positive and non-zero to compute the surface area accurately.
Q1: What is a Gyroelongated Square Pyramid?
A: A gyroelongated square pyramid is a Johnson solid constructed by attaching a square pyramid to a square antiprism, resulting in a complex polyhedron.
Q2: Why is the formula structured as (1 + 3√3) * le²?
A: The term (1 + 3√3) combines the contributions from the base and the triangular faces, with √3 arising from the geometry of equilateral triangles.
Q3: What units should be used for the edge length?
A: The edge length should be in meters (m) for the surface area to be in square meters (m²). Consistent units are crucial for accurate results.
Q4: Can this calculator handle very large or very small edge lengths?
A: Yes, as long as the input is a positive number, the calculator can process it, though extremely large values may lead to very large surface areas.
Q5: Is the TSA the same as the lateral surface area?
A: No, the total surface area includes all faces (base and lateral), whereas the lateral surface area only includes the side faces excluding the base.