Home Back

Inradius of Hexadecagon given Diagonal across Six Sides Calculator

Formula Used:

\[ r_i = \frac{d_6 \cdot \sin(\pi/16)}{\sin(3\pi/8)} \cdot \frac{1 + \sqrt{2} + \sqrt{2(2 + \sqrt{2})}}{2} \]

m

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is the Inradius of Hexadecagon?

The inradius of a hexadecagon (16-sided polygon) is the radius of the circle that fits perfectly inside the hexadecagon, touching all its sides. It represents the distance from the center of the hexadecagon to any of its sides.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \frac{d_6 \cdot \sin(\pi/16)}{\sin(3\pi/8)} \cdot \frac{1 + \sqrt{2} + \sqrt{2(2 + \sqrt{2})}}{2} \]

Where:

Explanation: This formula calculates the inradius based on the diagonal measurement across six sides, utilizing trigonometric functions and square roots to account for the geometric properties of a regular hexadecagon.

3. Importance of Inradius Calculation

Details: Calculating the inradius is essential for various geometric applications, including determining the area of the hexadecagon, understanding its spatial properties, and for applications in architecture and design where precise measurements are required.

4. Using the Calculator

Tips: Enter the diagonal across six sides of the hexadecagon in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a hexadecagon?
A: A hexadecagon is a polygon with 16 sides and 16 angles. It is a regular polygon when all sides and angles are equal.

Q2: How is the diagonal across six sides measured?
A: The diagonal across six sides is the straight line distance between two non-adjacent vertices that are six sides apart on the hexadecagon.

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

Q4: What are practical applications of hexadecagon calculations?
A: Hexadecagons are used in architecture, engineering design, and various mathematical studies of geometric properties.

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

Inradius of Hexadecagon given Diagonal across Six Sides Calculator© - All Rights Reserved 2025