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Height of Gyroelongated Square Pyramid Calculator

Formula Used:

\[ h = \left( \sqrt{1 - \frac{1}{2 + \sqrt{2}}} + \frac{1}{\sqrt{2}} \right) \times l_e \]

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1. What is the Height of Gyroelongated Square Pyramid?

The Height of Gyroelongated Square Pyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Square Pyramid. It is an important geometric measurement in three-dimensional geometry and architectural design.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ h = \left( \sqrt{1 - \frac{1}{2 + \sqrt{2}}} + \frac{1}{\sqrt{2}} \right) \times l_e \]

Where:

Explanation: This formula combines square root functions and mathematical constants to calculate the precise height based on the edge length of the pyramid.

3. Importance of Height Calculation

Details: Accurate height calculation is crucial for architectural design, structural engineering, and geometric analysis of complex polyhedral shapes.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

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.

Q2: What units should I use for the edge length?
A: The calculator uses meters as the default unit, but you can use any consistent unit as long as you maintain consistency throughout your calculations.

Q3: How accurate is this calculation?
A: The calculation provides a precise mathematical result based on the geometric properties of the gyroelongated square pyramid.

Q4: Can this formula be used for other pyramid types?
A: No, this specific formula is designed only for gyroelongated square pyramids and cannot be applied to other pyramid geometries.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in architectural design, 3D modeling, mathematical education, and structural analysis of complex geometric shapes.

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