1. What is the Inradius of Pentagon?

The inradius of a pentagon is the radius of the inscribed circle that touches all five sides of 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 inradius formula:

Where:

• \( r_i \) — Inradius of the pentagon
• \( A \) — Area of the pentagon
• \( \sqrt{25+(10\sqrt{5})} \) — Mathematical constant for pentagon calculations

Explanation: The formula calculates the inradius based on the area of the pentagon using the geometric properties of regular pentagons.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle, which is useful in various engineering and design applications involving pentagonal shapes.

4. Using the Calculator

Tips: Enter the area of the pentagon in square meters. The value must be positive and greater than zero for accurate calculation.

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

Q4: What are practical applications of pentagon inradius?
A: Used in architecture, engineering design, and various mathematical problems involving pentagonal shapes and their properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular pentagons, with accuracy depending on the precision of the input area value.