1. What is a Regular Decagon?

A regular decagon is a ten-sided polygon where all sides are equal in length and all angles are equal. It has ten lines of symmetry and rotational symmetry of order 10.

2. How Does the Calculator Work?

The calculator uses the regular decagon area formula:

Where:

• \( A \) — Area of the decagon
• \( s \) — Length of one side
• \( \cot \) — Cotangent trigonometric function
• \( \pi \) — Pi (approximately 3.14159)

Explanation: The formula calculates the area by dividing the decagon into 10 congruent isosceles triangles and summing their areas.

3. Importance of Decagon Calculations

Details: Calculating the area of regular decagons is important in geometry, architecture, and design where this symmetrical shape is used.

4. Using the Calculator

Tips: Enter the side length in any units (all measurements must use the same units). The result will be in square units of whatever unit you used for the side length.

5. Frequently Asked Questions (FAQ)

Q1: What is the interior angle of a regular decagon?
A: Each interior angle measures 144 degrees in a regular decagon.

Q2: What is the exact value of cot(π/10)?
A: \( \cot(\pi/10) = \sqrt{5 + 2\sqrt{5}} \), approximately 3.07768.

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

Q4: What are some real-world examples of decagons?
A: Decagonal shapes appear in some coins, architectural designs, and decorative patterns.

Q5: How does the area change with side length?
A: The area increases with the square of the side length (double the side length = 4× the area).