1. What is the Height of Decagon given Circumradius Formula?

The formula calculates the height of a regular decagon when its circumradius is known. A decagon is a ten-sided polygon, and this formula provides the perpendicular distance from one side to the opposite vertex.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Decagon (m)
• \( r_c \) — Circumradius of Decagon (m)

Explanation: The formula derives from geometric properties of regular decagons and trigonometric relationships between the circumradius and height.

3. Importance of Height Calculation

Details: Calculating the height of a decagon is important in geometry, architecture, and engineering applications where precise dimensional relationships are required for regular polygonal structures.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a ten-sided polygon where all sides are equal in length and all interior angles are equal (144 degrees each).

Q2: What is circumradius?
A: Circumradius is the radius of a circle that passes through all vertices of a polygon. For a regular decagon, it's the distance from the center to any vertex.

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

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, engineering projects, and geometric modeling where decagonal shapes are employed.

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular decagons and provides precise results when accurate input values are used.