Suppose a polygon has n vertices (and sides). From each vertex, a diagonal can be drawn to all vertices, excluding itself and the two adjacent vertices. So n-3 diagonals can be drawn from each vertex. Multiplying by the full complement of n vertices gives n(n-3). However, as things stand we have counted each diagonal twice: once at both ends. Dividing by two gives the actual number of diagonals. number of diagonals = n(n-3)/2
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You can find the number of diagonals in a polygon using the formula n(n-3)/2, where n is the number of sides. Therefore an 11 sided polygon has 44 diagonals.
It is: 0.5*(n2-3n) = diagonals whereas 'n' is the number of sides of the polygon
A polygon that has 104 diagonals will have 16 sides
The formula used to find the number of diagonals in a polygon is n(n-3)/2. 30 x 27/2 = 810/2 = 405 diagonals.
Use the formula of: 0.5*(n2-3n) whereby n is the number of sides of the polygon