1. What is the Area of Pentagon given Inradius?

The Area of Pentagon given Inradius is the amount of two-dimensional space taken up by a Pentagon, calculated using the inradius (the radius of the circle inscribed inside the Pentagon).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of Pentagon (m²)
• \( r_i \) — Inradius of Pentagon (m)

Explanation: This formula calculates the area of a regular pentagon using its inradius, incorporating the mathematical constant √5.

3. Importance of Pentagon Area Calculation

Details: Calculating the area of a pentagon is important in geometry, architecture, and various engineering applications where pentagonal shapes are used.

4. Using the Calculator

Tips: Enter the inradius value 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: 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: Can this formula be used for irregular pentagons?
A: No, this formula is specifically for regular pentagons. Irregular pentagons require different methods for area calculation.

Q4: What are some real-world applications of pentagons?
A: Pentagons are used in architecture (e.g., the Pentagon building), design, and various mathematical and geometric applications.

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