1. What is the Side of Decagon given Diagonal across Two Sides Formula?

The formula calculates the side length of a regular decagon when the diagonal across two sides is known. A decagon is a ten-sided polygon, and this formula provides a precise mathematical relationship between the side length and the specified diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side of Decagon (m)
• \( d_2 \) — Diagonal across Two Sides of Decagon (m)

Explanation: The formula derives from geometric properties of regular decagons and involves the mathematical constant √5.

3. Importance of Decagon Side Calculation

Details: Calculating the side length of a decagon is important in geometry, architecture, and design where regular decagonal shapes are used. It helps in precise measurements and construction.

4. Using the Calculator

Tips: Enter the diagonal across two sides in meters. The value must be positive and greater than zero.

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

Q3: Can this calculator be used for irregular decagons?
A: No, this formula only applies to regular decagons where all sides and angles are equal.

Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, engineering projects, and mathematical geometry problems involving decagons.

Q5: Why does the formula contain √5?
A: The √5 appears due to the mathematical relationships in pentagonal symmetry, which is fundamental to decagon geometry.