1. What is the Side of Decagon given Height Formula?

The formula calculates the side length of a regular decagon when its height is known. A decagon is a ten-sided polygon, and this formula provides the relationship between its height and side length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( S \) — Side length of the decagon (m)
• \( h \) — Height of the decagon (m)

Explanation: The formula derives from the geometric properties of a regular decagon, using the square root function to establish the relationship between height and side length.

3. Importance of Side Calculation

Details: Calculating the side length from height is essential in geometry, architecture, and design where decagonal shapes are used. It helps in precise measurements and construction planning.

4. Using the Calculator

Tips: Enter the height of the decagon in meters. The value must be positive and valid. The calculator will compute the corresponding side length.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a polygon with ten equal sides and ten equal angles.

Q2: Why is the formula involving square roots?
A: The square roots come from the trigonometric relationships and the golden ratio properties inherent in a regular decagon.

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

Q4: What are practical applications of this calculation?
A: It's used in architectural design, engineering projects, and any field requiring precise geometric calculations with decagonal shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular decagons, though practical measurements may have slight variations.