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Diagonal Of Decagon Across Three Sides Given Width Calculator

Formula Used:

\[ Diagonal across Three Sides of Decagon = \frac{\sqrt{14 + 6\sqrt{5}} \times Width of Decagon}{2(1 + \sqrt{5})} \]

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1. What is Diagonal across Three Sides of Decagon?

Diagonal across Three Sides of Decagon is a straight line joining two non-adjacent sides which is across three sides of the Decagon.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Diagonal across Three Sides of Decagon = \frac{\sqrt{14 + 6\sqrt{5}} \times Width of Decagon}{2(1 + \sqrt{5})} \]

Where:

3. Formula Explanation

Details: This formula calculates the diagonal length across three sides of a regular decagon based on its width. The formula incorporates the mathematical constant √5 and follows geometric relationships specific to decagons.

4. Using the Calculator

Tips: Enter the width of the decagon in meters. The value must be a positive number greater than zero.

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: How is width defined for a decagon?
A: Width of a decagon is the measurement from side to side at the widest point of the shape.

Q3: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering, and design where decagonal shapes are used.

Q4: Can this formula be used for irregular decagons?
A: No, this formula applies only to regular decagons where all sides and angles are equal.

Q5: What units should be used for the input?
A: The calculator accepts meters as input, but any consistent unit of length can be used as the result will be in the same units.

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