Ridge Length of Star Pyramid Calculator

Formula Used:

\[ Ridge\ Length = \sqrt{\left(\frac{Pentagonal\ Edge\ Length^2}{100} \times (50 + (10 \times \sqrt{5}))\right) + Height^2} \]

Ridge Length of Star Pyramid:

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1. What is the Ridge Length of Star Pyramid?

The Ridge Length of a Star Pyramid is the length of the line joining any inner vertex of the pentagrammic base of the Star Pyramid and the apex of the Star Pyramid. It represents the slanted edge from the base to the peak of the pyramid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Ridge\ Length = \sqrt{\left(\frac{Pentagonal\ Edge\ Length^2}{100} \times (50 + (10 \times \sqrt{5}))\right) + Height^2} \]

Where:

Pentagonal Edge Length — Edge length of the regular pentagon from which the pentagrammic base is constructed (m)
Height — Perpendicular distance from the apex to the base of the Star Pyramid (m)
√5 — Square root of 5 (approximately 2.23607)

Explanation: The formula combines the geometric properties of the pentagrammic base with the pyramid's height to calculate the diagonal ridge length.

3. Importance of Ridge Length Calculation

Details: Calculating the ridge length is essential for architectural design, structural analysis, and understanding the geometric properties of star pyramids in various applications.

4. Using the Calculator

Tips: Enter the pentagonal edge length and height in meters. Both values must be positive numbers. The calculator will compute the ridge length using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Star Pyramid?
A: A Star Pyramid is a pyramid with a pentagram (five-pointed star) as its base and five triangular faces meeting at the apex.

Q2: How is the pentagonal edge length related to the star pyramid?
A: The pentagonal edge length refers to the edge of the regular pentagon from which the pentagrammic base is constructed, forming the foundation of the star pyramid.

Q3: What units should I use for the inputs?
A: The calculator uses meters for both pentagonal edge length and height. Ensure consistent units for accurate results.

Q4: Can this formula be used for other pyramid types?
A: No, this specific formula is designed for star pyramids with pentagrammic bases and incorporates the unique geometric properties of pentagrams.

Q5: What is the significance of the √5 term in the formula?
A: The √5 term comes from the golden ratio properties inherent in pentagonal geometry, which is fundamental to the construction of pentagrams.