1. What is the Diagonal across Five Sides of Decagon?

The diagonal across five sides of a decagon is a straight line joining two opposite vertices that spans across five sides of the regular decagon. It represents one of the longest diagonals in a decagon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( d5 \) — Diagonal across five sides of decagon (meters)
• \( d4 \) — Diagonal across four sides of decagon (meters)
• \( \sqrt{} \) — Square root function

3. Formula Explanation

Details: This formula establishes a precise mathematical relationship between the diagonal across four sides and the diagonal across five sides of a regular decagon, utilizing the golden ratio properties inherent in decagonal geometry.

4. Using the Calculator

Tips: Enter the diagonal across four sides of the decagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding diagonal across five sides.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a polygon with ten equal sides and ten equal angles.

Q2: How many diagonals does a decagon have?
A: A decagon has 35 diagonals in total, with different lengths depending on how many sides they span.

Q3: What is the relationship between d4 and d5?
A: The diagonal across five sides is approximately 1.05146 times longer than the diagonal across four sides in a regular decagon.

Q4: Can this formula be used for irregular decagons?
A: No, this formula applies only to regular decagons where all sides and angles are equal.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architectural design, and various engineering applications involving decagonal structures.