1. What is the Height of Octagon given Inradius?

The height of a regular octagon is the vertical distance from its bottom edge to its top edge. When the inradius (the radius of the inscribed circle) is known, the height can be calculated using a simple mathematical relationship.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: For a regular octagon, the height is exactly twice the inradius. This relationship holds true because the octagon is symmetric and the inradius extends from the center to the midpoint of a side.

3. Importance of Height Calculation

Details: Calculating the height of an octagon is essential in various architectural, engineering, and design applications where precise dimensions are required for construction and manufacturing.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero to get a valid height calculation.

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 in measure.

Q2: What is the inradius of an octagon?
A: The inradius is the radius of the circle that fits perfectly inside the octagon, touching all eight sides.

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 practical applications of this calculation?
A: This calculation is useful in architecture, engineering design, manufacturing, and any field that works with geometric shapes and precise measurements.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular octagons, providing precise results when accurate input values are provided.