1. What is the Inradius of a Decagon?

The inradius of a decagon is the radius of the inscribed circle that touches all ten sides of the regular decagon from the inside. It represents the distance from the center of the decagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the inradius formula for a regular decagon:

Where:

• \( r_i \) — Inradius of the decagon
• \( A \) — Area of the decagon
• \( \sqrt{5 + 2\sqrt{5}} \) — Mathematical constant specific to decagon geometry

Explanation: This formula calculates the inradius based on the given area of a regular decagon, using the mathematical relationship between area and inscribed circle radius.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and various practical applications such as architectural design, engineering, and manufacturing where decagonal shapes are used. It helps determine the maximum size of objects that can fit inside the decagon without touching its sides.

4. Using the Calculator

Tips: Enter the area of the decagon in square meters. The area must be a positive value greater than zero. The calculator will compute the corresponding inradius of the regular 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: How is the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching the sides), while the circumradius is the radius of the circumscribed circle (passing through the vertices).

Q3: Can this formula be used for irregular decagons?
A: No, this formula is specifically for regular decagons where all sides and angles are equal. Irregular decagons require different calculation methods.

Q4: What are practical applications of decagon geometry?
A: Decagonal shapes are used in architecture (building designs), engineering (bolt heads, nuts), design (patterns and decorations), and various mechanical components.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular decagons. The accuracy of the result depends on the precision of the input area value.