1. What is Inradius of Decagon?

The Inradius of a Decagon is the length of the straight line from the center to any point on the incircle of the Decagon. It represents the radius of the largest circle that fits inside the decagon.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Decagon (m)
• \( d_4 \) — Diagonal across Four Sides of Decagon (m)

Explanation: The inradius of a regular decagon is exactly half the length of the diagonal that spans across four sides of the decagon.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and various engineering applications where the dimensions of inscribed circles within regular polygons need to be determined for design and construction purposes.

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.

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: How is the diagonal across four sides defined?
A: The diagonal across four sides is a straight line joining two non-adjacent vertices that spans across four sides of the decagon.

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 architecture, engineering design, and various geometric constructions involving regular decagonal shapes.

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