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The total number of diagonals for a convex (or concave) polygon, a hexagon being of the former type, is given by the equation (n2 - 3n)/2, where n is the number of sides of the polygon. A hexagon has 6 sides, so plugging the number 6 into the above equation for n, one finds that a hexagon has:

[62 - 3(6)]/2 = (36 - 18)/2 = 18/2 = 9 diagonals.

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