1. What is Apothem of a Pentagon?

The apothem of a regular pentagon is the line segment from the center to the midpoint of one of its sides. It is perpendicular to that side and represents the radius of the inscribed circle of the pentagon.

2. How Does the Calculator Work?

The calculator uses the apothem formula:

Where:

• \( a \) — Apothem length
• \( side \) — Length of one side of the pentagon
• \( 36^\circ \) — Half of the central angle (72°/2)

Explanation: The formula derives from the trigonometric relationships in a regular pentagon, where each interior angle is 108° and each central angle is 72°.

3. Importance of Apothem Calculation

Details: The apothem is crucial for calculating the area of a regular pentagon using the formula: Area = (Perimeter × Apothem)/2. It's also important in various geometric and architectural applications.

4. Using the Calculator

Tips: Enter the side length of the regular pentagon. The value must be positive. The calculator will compute the apothem length using the trigonometric formula.

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: Can this calculator be used for irregular pentagons?
A: No, this calculator is specifically designed for regular pentagons where all sides and angles are equal.

Q3: What units should I use for the side length?
A: You can use any unit of length (cm, inches, meters, etc.), but be consistent as the apothem will be in the same units.

Q4: How is the apothem related to the radius?
A: The apothem is the radius of the inscribed circle (incircle) of the pentagon, which touches each side at its midpoint.

Q5: What if my pentagon is not regular?
A: For irregular pentagons, there is no single apothem formula. You would need to use different geometric methods based on the specific shape.