1. What Is The Inradius Of Octagon Given Height?

The inradius of an octagon is the radius of the incircle that touches all eight sides of the regular octagon. Given the height of the octagon, the inradius can be calculated using a simple formula.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Octagon (m)
• \( h \) — Height of Octagon (m)

Explanation: The formula shows that the inradius of a regular octagon is exactly half of its height. This relationship holds true for all regular octagons.

3. Importance Of Inradius Calculation

Details: Calculating the inradius is important in geometry and various practical applications such as construction, design, and engineering where octagonal shapes are used.

4. Using The Calculator

Tips: Enter the height of the octagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octagon?
A: A regular octagon is an eight-sided polygon where all sides are equal in length and all angles are equal.

Q2: How is the height of an octagon measured?
A: The height of a regular octagon is the vertical distance between its top and bottom edges when oriented with one side horizontal.

Q3: Can this formula be used for irregular octagons?
A: No, this formula only applies to regular octagons where all sides and angles are equal.

Q4: What are some practical applications of octagons?
A: Octagons are commonly used in architecture (stop signs, building designs), engineering, and various decorative patterns.

Q5: How does the inradius relate to other octagon measurements?
A: The inradius is directly related to the side length and apothem of the octagon, and can be used to calculate other geometric properties.