Polygon Diagonal Calculator
Number of Diagonals: -
Interior Angle: -°
Understanding Polygon Diagonals
What are Polygon Diagonals?
A diagonal is a line segment that connects two non-adjacent vertices of a polygon.
Number of Diagonals = [n(n-3)]/2
Interior Angle = [(n-2) × 180°]/n
where:
- n = number of sides
- Each vertex connects to (n-3) other vertices
- Total is divided by 2 to avoid counting twice
Properties of Diagonals
- All diagonals are inside a convex polygon
- Each vertex connects to all non-adjacent vertices
- Number of diagonals increases quadratically with sides
- Regular polygons have equal-length diagonals from center
Common Polygon Properties
Triangle (n=3)
0 diagonals
Square (n=4)
2 diagonals
Pentagon (n=5)
5 diagonals
Hexagon (n=6)
9 diagonals
Special Cases
| Polygon Type | Diagonals | Interior Angle |
|---|---|---|
| Triangle | 0 | 60° |
| Square | 2 | 90° |
| Regular Pentagon | 5 | 108° |
| Regular Hexagon | 9 | 120° |
Real-World Applications
Architecture
Structural design and space planning
Computer Graphics
Polygon mesh modeling and rendering
Game Development
Collision detection and pathfinding
Engineering
Material optimization and design