1. What is Diagonal across Five Sides of Decagon?

Diagonal across Five Sides of Decagon is a straight line joining two opposite sides which is across five sides of the Decagon. It represents the longest diagonal in a regular decagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d5 \) — Diagonal across Five Sides of Decagon (m)
• \( d3 \) — Diagonal across Three Sides of Decagon (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

3. Formula Explanation

Mathematical Basis: This formula is derived from the geometric properties of a regular decagon and the golden ratio relationship between its various diagonals. The formula uses the mathematical constant √5 which is fundamental to decagon geometry.

4. Using the Calculator

Instructions: Enter the length of the diagonal across three sides of the decagon in meters. The value must be positive. Click Calculate to get the diagonal across five sides.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between d3 and d5 in a decagon?
A: In a regular decagon, the diagonal across five sides (d5) is the longest diagonal and is related to the diagonal across three sides (d3) through the golden ratio and specific geometric proportions.

Q2: Can this formula be used for irregular decagons?
A: No, this formula applies only to regular decagons where all sides and angles are equal.

Q3: What are typical applications of this calculation?
A: This calculation is used in geometry, architectural design, and engineering where decagonal shapes are employed.

Q4: How accurate is this formula?
A: The formula is mathematically exact for regular decagons and provides precise results.

Q5: What units should be used for input?
A: The calculator accepts any consistent unit of length, though meters are displayed. The result will be in the same units as the input.