In a regular polygon with ( n ) sides, the number of non-intersecting diagonals that can be drawn is given by the formula ( \frac{n(n-3)}{2} ). However, if you are looking for the number of ways to draw non-intersecting diagonals that divide the polygon into triangles (triangulation), the count is represented by the ( (n-2) )-th Catalan number, which is ( C_{n-2} = \frac{1}{n-1} \binom{2(n-2)}{n-2} ). Thus, the interpretation of "non-intersecting diagonals" can vary based on context.
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The diagonals (drawn from a point) help in dividing the regular polygon into smaller triangles. The sum of the areas of these smaller triangles help in determining the total area of the polygon.
You can use the formula D=S-2 where D is the number of possible diagonals and S is the number of sides the polygon has.
A 5-sided polygon is called a pentagon. You can draw up to 5 diagonals in a pentagon.
It works out that a polygon with 1175 diagonals has 50 sides
1/2*(142-42) = 77 diagonals