Lateral Edge Length of Star Pyramid given Ridge Length Calculator

Formula Used:

\[ l_{lateral} = \sqrt{\left(\frac{l_c^2}{100} \times (50 + 10\sqrt{5})\right) + l_{ridge}^2 - \left(\frac{l_{pentagon}^2}{100} \times (50 + 10\sqrt{5})\right)} \]

Chord Length of Star Pyramid (l_c):

Ridge Length of Star Pyramid (l_ridge):

Pentagonal Edge Length of Base (l_pentagon):

Lateral Edge Length of Star Pyramid:

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1. What is the Lateral Edge Length of Star Pyramid?

The Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid. It represents the slanted edge from the base perimeter to the pyramid's peak.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_{lateral} = \sqrt{\left(\frac{l_c^2}{100} \times (50 + 10\sqrt{5})\right) + l_{ridge}^2 - \left(\frac{l_{pentagon}^2}{100} \times (50 + 10\sqrt{5})\right)} \]

Where:

\( l_{lateral} \) — Lateral Edge Length (m)
\( l_c \) — Chord Length of Star Pyramid (m)
\( l_{ridge} \) — Ridge Length of Star Pyramid (m)
\( l_{pentagon} \) — Pentagonal Edge Length of Base (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the lateral edge length based on the geometric relationships between the chord length, ridge length, and pentagonal edge length of a star pyramid.

3. Importance of Lateral Edge Length Calculation

Details: Calculating the lateral edge length is essential for architectural design, geometric modeling, and structural analysis of star pyramid shapes. It helps determine the overall dimensions and proportions of the pyramid structure.

4. Using the Calculator

Tips: Enter all three length values in meters. Ensure all values are positive numbers greater than zero for accurate calculation results.

5. Frequently Asked Questions (FAQ)

Q1: What is a Star Pyramid?
A: A Star Pyramid is a pyramid with a star-shaped base, typically constructed from a pentagram inscribed in a regular pentagon.

Q2: How is Chord Length different from Pentagonal Edge Length?
A: Chord Length is the distance between two adjacent spike points of the star base, while Pentagonal Edge Length is the side length of the underlying regular pentagon.

Q3: What is Ridge Length in a Star Pyramid?
A: Ridge Length is the distance from any inner vertex of the star base to the apex of the pyramid.

Q4: Can this formula be used for any star pyramid?
A: This specific formula applies to star pyramids with a pentagrammic base constructed from a regular pentagon.

Q5: What are practical applications of this calculation?
A: This calculation is used in architectural design, monument construction, geometric art, and mathematical modeling of three-dimensional star-shaped structures.