1. What is the Inradius of Pentagon?

The inradius of a pentagon is the radius of the circle that fits perfectly inside the pentagon, touching all five sides. It represents the distance from the center of the pentagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of the pentagon
• \( d \) — Diagonal of the pentagon
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the inradius based on the diagonal measurement of a regular pentagon, using the mathematical relationship between these geometric properties.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry, architecture, and engineering for determining the size of inscribed circles, designing circular components within pentagonal structures, and solving various geometric problems involving regular pentagons.

4. Using the Calculator

Tips: Enter the diagonal length of the pentagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding inradius.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular pentagon?
A: A regular pentagon is a five-sided polygon where all sides are equal in length and all interior angles are equal (108 degrees each).

Q2: How is the diagonal related to the inradius?
A: The diagonal and inradius have a fixed mathematical relationship in a regular pentagon, allowing one to be calculated from the other using specific formulas.

Q3: Can this calculator be used for irregular pentagons?
A: No, this calculator is specifically designed for regular pentagons 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 geometric modeling where pentagonal shapes with inscribed circles are required.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact for regular pentagons, though the displayed result is rounded to six decimal places for practical use.