1. What is a Pentagon?

A pentagon is a five-sided polygon with five angles. In a regular pentagon, all sides are equal in length and all interior angles are equal (108° each). The area of a regular pentagon can be calculated using a specific formula involving the side length.

2. How Does the Calculator Work?

The calculator uses the regular pentagon area formula:

Where:

• \( A \) — Area of the pentagon
• \( s \) — Length of one side
• \( \sqrt{5(5+2\sqrt{5})} \) — Constant (~7.694)

Explanation: The formula calculates the area by multiplying a constant (derived from pentagon geometry) by the square of the side length.

3. Importance of Pentagon Calculations

Details: Calculating pentagon properties is essential in geometry, architecture, and design. The regular pentagon appears in nature (e.g., starfish) and human designs (e.g., the Pentagon building).

4. Using the Calculator

Tips: Enter the side length of your regular pentagon in any units. The calculator will provide area, perimeter, and diagonal length in the same units squared or linear units.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for irregular pentagons?
A: No, this calculator is only for regular pentagons where all sides and angles are equal.

Q2: What's the interior angle of a regular pentagon?
A: Each interior angle is 108° in a regular pentagon.

Q3: How is the diagonal calculated?
A: The diagonal of a regular pentagon is the side length multiplied by the golden ratio (1 + √5)/2 ≈ 1.618.

Q4: What's the apothem of a pentagon?
A: The apothem (a) can be calculated as a = s/(2 tan(π/5)) ≈ s/1.453.

Q5: Can I calculate side length from area?
A: Yes, you can rearrange the formula: s = √(4A/√(5(5+2√5))).