1. What is the Inradius of Pentagon?

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon. 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 Pentagon (m)
• \( w \) — Width of Pentagon (m)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the inradius of a regular pentagon based on its width, using mathematical constants and square root functions.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry and engineering for determining the size of inscribed circles within pentagonal shapes, which has applications in various design and construction projects.

4. Using the Calculator

Tips: Enter the width of the pentagon in meters. The value must be positive and greater than zero.

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 width defined for a pentagon?
A: The width of a pentagon is the measurement or extent of horizontal distance from left to right of the pentagon.

Q3: What are the practical applications of this calculation?
A: This calculation is used in architecture, engineering design, and various geometric applications where pentagonal shapes are involved.

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

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular pentagons, though real-world measurements may introduce some margin of error.