1. What is the Area of Pentagon Formula?

The formula calculates the area of a regular pentagon using its inradius. A regular pentagon is a five-sided polygon with all sides and angles equal, and the inradius is the radius of the inscribed circle.

2. How Does the Calculator Work?

The calculator uses the pentagon area formula:

Where:

• \( A \) — Area of Pentagon (m²)
• \( r_i \) — Inradius of Pentagon (m)
• \( \pi \) — Mathematical constant pi (≈3.14159)
• \( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the area by multiplying the square of the inradius by 5 times the tangent of π/5 radians (36 degrees).

3. Importance of Pentagon Area Calculation

Details: Calculating the area of a pentagon is essential in geometry, architecture, engineering, and various design 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 for accurate calculation.

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 only applies to regular pentagons where all sides and angles are equal.

Q4: What are some real-world applications of pentagon area calculation?
A: Pentagon area calculations are used in architecture (pentagonal buildings), design (pentagonal patterns), and various engineering 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 value.