1. What is the Pentagon Side Formula?

The pentagon side formula calculates the side length of a regular pentagon given its apothem (the distance from the center to the midpoint of a side). For a regular pentagon, all sides and angles are equal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Apothem (distance from center to side midpoint)
• \( 36^\circ \) — Half of the central angle (72°/2)

Explanation: The formula derives from the trigonometric relationship in a right triangle formed by the apothem, half the side, and the radius to a vertex.

3. Importance of Pentagon Side Calculation

Details: Calculating side lengths is essential in geometry, architecture, engineering, and design where pentagonal shapes are used. It helps in material estimation and structural design.

4. Using the Calculator

Tips: Enter the apothem length in any consistent units. The result will be in the same units. The apothem must be a positive value.

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° each).

Q2: What is the apothem of a pentagon?
A: The apothem is the perpendicular distance from the center of the pentagon to the midpoint of one of its sides.

Q3: Can I calculate the side if I know the radius instead?
A: Yes, the formula would be different: \( Side = 2R \times \sin(36^\circ) \) where R is the circumradius.

Q4: What are some real-world applications of pentagons?
A: Pentagons are used in architecture (like the Pentagon building), design patterns, military insignia, and various engineering applications.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect regular pentagon. The accuracy depends on the precision of the input value.