Finding the diagonal of a regular hexagon is straightforward, especially when referring to the longest diagonal that connects opposite vertices. The length of this principal diagonal is directly related to the side length of the hexagon.
Understanding Regular Hexagon Diagonals
A regular hexagon is a six-sided polygon with all sides and all internal angles equal. It possesses two types of diagonals:
- Short diagonals: Connecting alternate vertices (skipping one vertex).
- Long diagonals: Connecting opposite vertices (passing through the center of the hexagon).
When people refer to "the diagonal" of a regular hexagon without specifying, they usually mean the long diagonal.
Calculating the Length of the Long Diagonal
According to mathematical principles and as referenced, the length of the long diagonal of a regular hexagon is exactly twice the length of its side.
Here is the formula based on the provided information:
Length of the long diagonal of a regular hexagon = 2 × side length
This relationship exists because a regular hexagon can be divided into six equilateral triangles by lines drawn from the center to each vertex. The side length of the hexagon is equal to the side length of these triangles. The long diagonal is simply the sum of the sides of two opposing equilateral triangles sharing the central point, making its length equal to twice the side length of the hexagon (or twice the radius of the circumscribed circle).
Example Calculation
Let's use the example provided in the reference to illustrate the calculation:
If the side length of the regular hexagon is 6 units:
- Given: Side length = 6 units
- Formula: Length of the diagonal = 2 × side length
- Calculation: Length of the diagonal = 2 × 6 = 12 units
Therefore, the length of the long diagonal of a regular hexagon with a side length of 6 units is 12 units.
Summary Table
| Feature | Description | Formula/Value |
|---|---|---|
| Polygon Type | Regular Hexagon | - |
| Diagonal Type | Long Diagonal (connecting opposite vertices) | - |
| Calculation Formula | Twice the side length | Diagonal = 2 * side |
| Example Side Length | 6 units | - |
| Example Diagonal Length | 12 units | 2 * 6 = 12 units |
This method provides a simple and exact way to find the length of the main diagonal of any regular hexagon, given its side length.
