1. What is 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 formula:

Where:

• \( d_5 \) — Diagonal across five sides of decagon (m)
• \( r_i \) — Inradius of decagon (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the diagonal length based on the inradius (distance from center to midpoints of sides) of a regular decagon.

3. Importance of Diagonal Calculation

Details: Calculating diagonals in polygons is important in geometry, architecture, and engineering for structural analysis, design optimization, and spatial planning.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a ten-sided polygon with all sides equal in length and all interior angles equal (144 degrees each).

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 inradius and side length?
A: For a regular decagon, the inradius is related to the side length by the formula: \( r_i = \frac{s}{2} \times \sqrt{5 + 2\sqrt{5}} \).

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

Q5: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric pattern creation where decagonal shapes are employed.