1. What is the Diagonal of Pentagon?

The diagonal of a pentagon is a straight line joining two non-adjacent vertices of the pentagon. In a regular pentagon, all diagonals are equal in length and intersect at specific angles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the diagonal length of a regular pentagon based on its inradius (the radius of the inscribed circle).

3. Importance of Diagonal Calculation

Details: Calculating the diagonal of a pentagon is important in geometry, architecture, and design applications where pentagonal shapes are used. It helps in determining proportions and spatial relationships.

4. Using the Calculator

Tips: Enter the inradius 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 inradius different from circumradius?
A: Inradius is the radius of the circle inscribed inside the pentagon (touching all sides), while circumradius is the radius of the circle that passes through all vertices.

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

Q4: What are some real-world applications of pentagon diagonals?
A: Pentagon diagonals are used in architectural design, military symbols (pentagon shape), and various geometric constructions.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular pentagons, though the displayed result may be rounded for practical purposes.