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 is the distance from the center of the pentagon to the midpoint of any side.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Height\ of\ Pentagon \) — The distance between one side of Pentagon and its opposite vertex (in meters)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \cos \) — Cosine trigonometric function

3. Formula Explanation

Details: This formula calculates the inradius of a regular pentagon using its height and the interior angle properties. The expression \( \cos\left(\frac{3}{5}\pi\right) \) relates to the cosine of 108 degrees, which is the interior angle of a regular pentagon.

4. Using the Calculator

Tips: Enter the height of the pentagon in meters. The height must be a positive value greater than 0.

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 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 practical applications of calculating pentagon inradius?
A: This calculation is useful in architecture, engineering design, and various geometric computations involving pentagonal shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular pentagons, using the exact trigonometric relationships.