Inradius Of Hendecagon Given Diagonal Across Four Sides Calculator

Formula Used:

\[ Inradius = \frac{\left(\frac{Diagonal \times \sin(\pi/11)}{\sin(4\pi/11)}\right)}{2 \times \tan(\pi/11)} \]

Inradius of Hendecagon:

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1. What is Inradius of Hendecagon?

The inradius of a hendecagon (11-sided polygon) is the radius of the circle that fits perfectly inside the polygon, touching all its sides. It represents the distance from the center to any side of the hendecagon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Inradius = \frac{\left(\frac{Diagonal \times \sin(\pi/11)}{\sin(4\pi/11)}\right)}{2 \times \tan(\pi/11)} \]

This formula calculates the inradius based on the diagonal measurement across four sides of the hendecagon.

3. Formula Explanation

The formula incorporates trigonometric functions to establish the relationship between the diagonal across four sides and the inradius:

Uses sine and tangent trigonometric functions
Incorporates π/11 and 4π/11 angles specific to hendecagon geometry
Provides accurate inradius calculation based on diagonal measurement

4. Using the Calculator

Instructions: Enter the diagonal measurement across four sides of the hendecagon in meters. The value must be greater than zero. Click calculate to get the inradius result.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is an 11-sided polygon, also known as an undecagon.

Q2: Why use this specific formula?
A: This formula provides the most accurate calculation of inradius when the diagonal across four sides is known, using trigonometric relationships specific to the hendecagon's geometry.

Q3: What units should I use?
A: Use consistent units (typically meters) for both input and output. The calculator assumes the same unit for diagonal measurement and inradius result.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision for accurate calculations.

Q5: What if I get an error message?
A: Ensure you've entered a positive numerical value for the diagonal measurement and that all required fields are filled.