Height Of Hendecagon Given Diagonal Across Four Sides Calculator

Formula Used:

\[ Height = \frac{\left(\frac{Diagonal\ Across\ Four\ Sides \times \sin(\pi/11)}{\sin(4\pi/11)}\right)}{2 \times \tan(\pi/22)} \]

Height of Hendecagon:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Height of Hendecagon?

The height of a hendecagon (11-sided polygon) is the perpendicular distance from one side to the opposite vertex. It's an important geometric measurement that helps in various calculations related to the polygon's area and other properties.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Height = \frac{\left(\frac{Diagonal\ Across\ Four\ Sides \times \sin(\pi/11)}{\sin(4\pi/11)}\right)}{2 \times \tan(\pi/22)} \]

This formula calculates the height of a regular hendecagon based on the diagonal measurement across four of its sides.

3. Formula Explanation

Mathematical Components:

\(\pi\) - Mathematical constant (approximately 3.14159)
\(\sin\) - Sine trigonometric function
\(\tan\) - Tangent trigonometric function
Diagonal Across Four Sides - The straight line joining two non-adjacent vertices across four sides

The formula uses trigonometric relationships specific to an 11-sided polygon to derive the height from the given diagonal measurement.

4. Using the Calculator

Instructions: Enter the diagonal measurement across four sides of the hendecagon in meters. The value must be a positive number. Click "Calculate" to get the height result.

5. Frequently Asked Questions (FAQ)

Q1: What is a hendecagon?
A: A hendecagon is a polygon with 11 sides and 11 angles. It's also known as an undecagon.

Q2: Why is this formula specific to hendecagons?
A: The angles used in the trigonometric functions (π/11, 4π/11, π/22) are derived from the specific geometry of an 11-sided polygon.

Q3: Can this calculator be used for irregular hendecagons?
A: No, this calculator is designed for regular hendecagons where all sides and angles are equal.

Q4: What units should I use for the diagonal measurement?
A: The calculator accepts any consistent unit of measurement, but the result will be in the same units as the input.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and trigonometric functions, providing results accurate to six decimal places.