1. What is the Side of Decagon given Inradius Formula?

The formula calculates the side length of a regular decagon when its inradius (the radius of the inscribed circle) is known. It provides a mathematical relationship between these two geometric properties of a decagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side of Decagon (m)
• \( r_i \) — Inradius of Decagon (m)

Explanation: The formula derives from the geometric properties of a regular decagon and the relationship between its side length and the radius of its inscribed circle.

3. Importance of Side Calculation

Details: Calculating the side length of a decagon from its inradius is important in geometry, architecture, and various engineering applications where regular decagonal shapes are used.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and valid. The calculator will compute the corresponding side length of the decagon.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the inradius of a polygon?
A: The inradius is the radius of the inscribed circle (incircle) that touches all sides of the polygon from the inside.

Q3: Can this formula be used for irregular decagons?
A: No, this formula applies only 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, mechanical engineering, and any field that works with geometric shapes and patterns.

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular decagons and provides precise results when accurate input values are provided.