I can't find the formula for the sides of a polygon vs. the total diagonals that it has! ex: 3 sided polygon, 0 diagonals, 4 sided, 2 diags, 5 s, 5 d, 6 s, 9 d, 7 s, 14 d 8 s, 20d, etc.
someone please tell me the formula
http://mathforum.org/library/drmath/view/54874.html
To find the formula for the relationship between the number of sides of a polygon and its total number of diagonals, we need to understand the concept of diagonals in a polygon.
A diagonal is a line segment connecting two non-adjacent vertices (corners) of a polygon. Let's break down the process of finding the number of diagonals in a polygon:
1. Start with a 3-sided polygon (triangle). Since it has only three sides, there are no diagonals.
2. Move to a 4-sided polygon (quadrilateral). Imagine one diagonal connecting two opposite vertices to divide the quadrilateral into two triangles. Therefore, there are 2 diagonals.
3. For a 5-sided polygon (pentagon), choose any vertex. From that vertex, there are two adjacent vertices and two non-adjacent vertices. Connect the chosen vertex to each of the non-adjacent vertices to form two diagonals. Repeat this process starting from a different vertex, resulting in five diagonals in total.
4. Continue this reasoning for larger polygons. For a 6-sided polygon (hexagon), there are nine diagonals, for a 7-sided polygon (heptagon), there are 14 diagonals, and so on.
Based on this pattern, we can conclude that the formula to find the number of diagonals in a polygon with n sides is:
Number of diagonals = (n x (n-3))/2
Keep in mind that the formula divides the result by 2 since each diagonal is counted twice (once from each end).
To verify this formula, you can plug in the values of different polygons and calculate their diagonals using the formula.