1. What is the Width of Pentagon given Inradius Formula?

The formula calculates the width of a regular pentagon when its inradius (the radius of the inscribed circle) is known. It provides a geometric relationship between these two important pentagon measurements.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( w \) — Width of Pentagon (m)
• \( r_i \) — Inradius of Pentagon (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives from the geometric properties of regular pentagons and their relationship with the golden ratio.

3. Importance of Pentagon Width Calculation

Details: Calculating pentagon width from inradius is crucial in geometry, architecture, and engineering applications where pentagonal shapes are used. It helps in precise measurements and design calculations.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and valid. The calculator will compute the corresponding width of the pentagon.

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: What is the inradius of a pentagon?
A: The inradius is the radius of the circle that can be inscribed inside the pentagon, touching all five sides.

Q3: How is width defined for a pentagon?
A: The width of a pentagon is the horizontal distance between the leftmost and rightmost points of the shape.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, and geometric modeling where pentagonal shapes are employed.

Q5: Can this formula be used for irregular pentagons?
A: No, this formula applies only to regular pentagons where all sides and angles are equal.