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 to any side of the pentagon.

2. How Does the Calculator Work?

The calculator uses the inradius formula:

Where:

• \( r_i \) — Inradius of the pentagon
• \( A \) — Area of the pentagon
• \( \pi \) — Mathematical constant (approximately 3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the radius of the inscribed circle based on the area of the pentagon and the central angle properties of a regular pentagon.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining properties of inscribed circles, designing symmetrical patterns, and solving problems related to regular pentagons in various applications.

4. Using the Calculator

Tips: Enter the area of the pentagon in square 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 the inradius different from the circumradius?
A: The inradius is the radius of the inscribed circle (touching all sides), while the circumradius is the radius of the circumscribed circle (passing through all vertices).

Q3: Can this formula be used for irregular pentagons?
A: No, this formula applies only to regular pentagons where all sides and angles are equal.

Q4: What are practical applications of pentagon geometry?
A: Pentagon geometry is used in architecture, design, military symbols (e.g., The Pentagon building), and various mathematical problems.

Q5: How is the central angle used in this calculation?
A: The central angle (π/5 or 36 degrees) is fundamental to deriving the relationship between area and inradius in a regular pentagon.