Imagine drawing a diagonal from one of the vertices to all of the other vertices. Two of these lines would be the outer edge so we don't count those. We have just drawn 13 diagonals. Move to the next corner and draw again. Don't
count the outer two and don't re-count the one to the previous corner so we have 12. Each corner goes down by one so the answer is 13+ 12+ 11+...+ 3+ 2+ 1= 91.
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.
It works out that a polygon with 1175 diagonals has 50 sides
1/2*(142-42) = 77 diagonals
5 diagonals * * * * * That is not correct since two of these would be lines joining the vertex to adjacent vertices (one on either side). These are sides of the polygon, not diagonals. The number of diagonals from any vertex of a polygon with n sides is n-3.
It is: 0.5*(144-36) = 54 diagonals
38 diagonals
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.
It works out that a polygon with 1175 diagonals has 50 sides
1/2*(142-42) = 77 diagonals
5 diagonals * * * * * That is not correct since two of these would be lines joining the vertex to adjacent vertices (one on either side). These are sides of the polygon, not diagonals. The number of diagonals from any vertex of a polygon with n sides is n-3.
It has 9 sides and it can be an regular or a irregular polygon which is called a nonagon Check: 0.5*(81-27) = 27 diagonals
In a 54-sided polygon, 53 possible diagonals can be drawn from one vertex to another. These diagonals will not intersect. Therefore, the interior will be divided into 54 regions by the 53 diagonals plus the two sides of the original polygon that adjoin the vertex from which the diagonals are drawn.
It is: 0.5*(144-36) = 54 diagonals
pentagon
Number of sides minus two equals number of diagonals drawn from one vertex.
For a polygon with n sides, there would be n*(n-3)/2
The formula for the number of diagonals is: 0.5*(n^2-3n) whereas 'n' is the number of sides of the polygon