Total Surface Area of Gyroelongated Square Dipyramid Calculator

Formula Used:

\[ TSA = 4 \times \sqrt{3} \times Edge\ Length^2 \]

Total Surface Area (TSA):

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1. What is the Total Surface Area of Gyroelongated Square Dipyramid?

The Total Surface Area (TSA) of a Gyroelongated Square Dipyramid is the total area of all its faces. It is calculated using the formula: TSA = 4 × √3 × Edge Length².

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 4 \times \sqrt{3} \times Edge\ Length^2 \]

Where:

\( Edge\ Length \) — Length of any edge of the Gyroelongated Square Dipyramid (in meters)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula accounts for the geometric properties of the Gyroelongated Square Dipyramid, providing an accurate calculation of its total surface area.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important for various applications, including material estimation, structural analysis, and academic studies in geometry.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Gyroelongated Square Dipyramid?
A: A Gyroelongated Square Dipyramid is a polyhedron formed by attaching two square pyramids to a square antiprism.

Q2: Why is the formula multiplied by 4 and √3?
A: The constants 4 and √3 come from the geometric properties and symmetry of the Gyroelongated Square Dipyramid.

Q3: Can this calculator be used for other units?
A: The calculator uses meters as the default unit. For other units, ensure consistent conversion before input.

Q4: What if the edge length is zero or negative?
A: The edge length must be a positive number. Zero or negative values are not valid.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the formula, with results rounded to six decimal places for clarity.