1. What is a Decagon Apothem?

The apothem of a regular decagon is the line from the center to the midpoint of one of its sides, which is also the radius of the decagon's incircle. It's a key measurement in geometric calculations involving regular decagons.

2. How Does the Calculator Work?

The calculator uses the decagon apothem formula:

Where:

• \( s \) — Length of one side of the decagon
• \( \pi \) — Mathematical constant Pi (~3.14159)
• \( \tan \) — Trigonometric tangent function

Explanation: The formula derives from dividing the decagon into 10 congruent isosceles triangles and using trigonometric relationships.

3. Importance of Apothem Calculation

Details: The apothem is essential for calculating the area of a regular decagon (Area = ½ × perimeter × apothem) and for various geometric constructions and designs.

4. Using the Calculator

Tips: Enter the side length of a regular decagon in any units. The calculator will return the apothem in the same units. The side length must be a positive number.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between apothem and radius?
A: The radius goes to a vertex, while the apothem goes to the midpoint of a side. In a decagon, radius = apothem / cos(π/10).

Q2: Can I calculate the area with this?
A: Yes, area = (10 × side × apothem)/2 = 5 × side × apothem.

Q3: Does this work for irregular decagons?
A: No, this calculator only works for regular decagons where all sides and angles are equal.

Q4: How precise are the calculations?
A: Results are accurate to 4 decimal places, sufficient for most practical applications.

Q5: What are common uses of decagon calculations?
A: Architecture, design, engineering, and any field requiring precise geometric constructions.