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The number of diagonals in an N-gon (polygon with N sides) refers to the total number of line segments that can be drawn connecting non-adjacent vertices of the polygon. Diagonals are important in geometry for understanding polygon properties and relationships.
The calculator uses the formula:
Where:
Explanation: Each vertex can connect to (N-3) other vertices (excluding itself and adjacent vertices), and we divide by 2 to avoid counting each diagonal twice.
Details: Calculating diagonals is essential for understanding polygon geometry, determining internal structure, and solving problems in combinatorics and graph theory related to polygonal shapes.
Tips: Enter the number of sides of the polygon (must be 3 or greater). The calculator will compute the total number of diagonals possible in the given polygon.
Q1: What is the minimum number of sides for a polygon to have diagonals?
A: A polygon must have at least 4 sides to have diagonals. Triangles (3 sides) have no diagonals.
Q2: How many diagonals does a square have?
A: A square (4 sides) has 2 diagonals: (4×(4-3))/2 = 2.
Q3: How many diagonals does a pentagon have?
A: A pentagon (5 sides) has 5 diagonals: (5×(5-3))/2 = 5.
Q4: Can this formula be used for all regular polygons?
A: Yes, the formula works for both regular and irregular polygons as long as they are simple polygons (non-self-intersecting).
Q5: What is the maximum number of diagonals in a polygon?
A: There is no theoretical maximum - as the number of sides increases, the number of diagonals increases quadratically.