1. What is the Height of Decagon given Diagonal across Three Sides?

The height of a decagon is the perpendicular distance from one vertex to the opposite side. This calculator determines the height when given the diagonal measurement across three sides of the regular decagon.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( Diagonal_{3} \) — Diagonal measurement across three sides of the decagon (meters)
• \( \sqrt{} \) — Square root function

Explanation: This formula derives from the geometric properties of a regular decagon and the relationship between its height and diagonal measurements.

3. Importance of Height Calculation

Details: Calculating the height of a decagon is essential in geometry, architecture, and design applications where precise dimensional relationships are required for regular decagonal shapes.

4. Using the Calculator

Tips: Enter the diagonal measurement across three sides in meters. The value must be positive and valid for accurate 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 internal angles are equal (144 degrees each).

Q2: How is the diagonal across three sides defined?
A: The diagonal across three sides connects two vertices with exactly two vertices between them along the decagon's perimeter.

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 useful in architectural design, engineering projects, and geometric pattern creation involving decagonal shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for regular decagons, with accuracy depending on the precision of the input measurement.