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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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What is the Practical application for finding the number of diagonals in a regular polygon?
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.
What rule can be used to find number of diagonals that can be drawn from one vertex of regular 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.
How many diagonals can be drawn in a 5-sided polygon?
A 5-sided polygon is called a pentagon. You can draw up to 5 diagonals in a pentagon.
Total of 1175 diagonal can be drawn in a polygon?
It works out that a polygon with 1175 diagonals has 50 sides
How many diagonals can be drawn in a polygon of 14 sides?
1/2*(142-42) = 77 diagonals
