Hexagon (6 sides)
In a hexagon, each vertex can connect to all other non-adjacent vertices to form diagonals. Since a hexagon has 6 vertices, each vertex can form diagonals with the other 4 non-adjacent vertices. Therefore, each vertex of a hexagon can create 4 diagonals. This results in a total of 6 vertices x 4 diagonals = 24 diagonals in a hexagon.
5
The diagonals of a square bisect each corner or vertex of the square.
Three
n-3 from each vertex.
A hexagon can be divided into four triangles by drawing all of the diagonals from one vertex. Since a hexagon has six sides, drawing diagonals from one vertex creates three additional triangles, resulting in a total of four triangles (the original triangle formed by the vertex and two adjacent vertices, plus the three formed by the diagonals).
how many diagonals from a vertex a heptagon have
A hexagon has 9 diagonals. Each vertex of a n-sided polygon can be connected to n - 3 others with diagonals. Thus n(n - 3) possible diagonals. However, when Vertex A is connected to vertex C, vertex C is also connected to vertex A, thus each diagonal is counted twice. Thus: number_of_diagonals = n(n - 3)/2 = 6(6-3)/2 = 6x3/2 = 9
A nonagonal prism has two parallel nonagonal bases, each with 9 vertices. Each vertex of the nonagon connects to two adjacent vertices and to the corresponding vertex on the opposite base, leaving 6 vertices that can be connected diagonally. Since there are 9 vertices in the base, each vertex has 6 diagonals, resulting in a total of 6 diagonals per vertex in the nonagonal prism.
There are no 'diagonals' in a triangle. Each vertex is connected to both of the other vertices, by the sides.
47 sides. Take a vertex of an n-sided polygon. There are n-1 other vertices. It is already joined to its 2 neighbours, leaving n-3 other vertices not connected to it. Thus n-3 diagonals can be drawn in from each vertex. For n=50, n-3 = 50-3 = 47 diagonals can be drawn from each vertex. The total number of diagonals in an n-sided polygon would imply n-3 diagonals from each of the n vertices giving n(n-3). However, the diagonal from vertex A to C would be counted twice, once for vertex A and again for vertex C, thus there are half this number of diagonals, namely: number of diagonals in an n-sided polygon = n(n-3)/2.
In a 15-gon, each vertex can connect to other vertices to form diagonals. Specifically, a vertex can connect to (15 - 3 = 12) other vertices (excluding itself and its two adjacent vertices). Therefore, from one vertex of a 15-gon, 12 diagonals can be drawn.