Diagonal Of Hendecagon Across Four Sides Given Inradius Calculator

Formula Used:

\[ Diagonal\ across\ Four\ Sides\ of\ Hendecagon = 2 \times \tan(\pi/11) \times Inradius\ of\ Hendecagon \times \sin((4 \times \pi)/11)/\sin(\pi/11) \]

Diagonal across Four Sides of Hendecagon:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Diagonal across Four Sides of Hendecagon?

The diagonal across four sides of a hendecagon is the straight line joining two non-adjacent vertices that are separated by four sides of the regular 11-sided polygon.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_4 = 2 \times \tan(\pi/11) \times r_i \times \sin((4 \times \pi)/11)/\sin(\pi/11) \]

Where:

\( d_4 \) — Diagonal across four sides of hendecagon
\( r_i \) — Inradius of the hendecagon
\( \pi \) — Archimedes' constant (approximately 3.14159)

3. Formula Explanation

Details: This formula calculates the length of the diagonal that spans across four sides of a regular hendecagon based on its inradius (the radius of the inscribed circle). The formula incorporates trigonometric functions to account for the geometric properties of the 11-sided polygon.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding diagonal length across four sides of the hendecagon.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. When all sides and angles are equal, it's called a regular hendecagon.

Q2: What is the inradius of a polygon?
A: The inradius is the radius of the largest circle that can fit inside the polygon, touching all its sides.

Q3: How accurate is this calculation?
A: The calculation uses precise mathematical constants and trigonometric functions, providing high accuracy for geometric computations.

Q4: Can this formula be used for irregular hendecagons?
A: No, this formula is specifically designed for regular hendecagons where all sides and angles are equal.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in geometry, architecture, engineering, and design where precise measurements of polygonal shapes are required.