Eight triangles.
50
A regular decagon can be divided into triangles by drawing diagonals from one vertex to all other non-adjacent vertices. This method results in a total of 8 triangles. Alternatively, using the formula for the number of triangles formed in a polygon, which is ( n - 2 ) (where ( n ) is the number of sides), a decagon (10 sides) can be divided into ( 10 - 2 = 8 ) triangles.
120 triangles.
13 triangles will be formed
There are 48 triangles that can be formed because 6 triangles can be formed usin each point multiplied by 8.
10 triangles....
A cube has 8 vertices, and to form a triangle, we need to select 3 vertices. However, to ensure that the selected vertices do not lie on the same face, we can only select vertices that are not all on the same plane. The valid combinations of vertices that can form a triangle while avoiding faces result in 0 possibilities since any selection of 3 vertices from a cube will always include at least one face. Therefore, no triangles can be formed by joining the vertices of a cube that do not lie on the faces.
There are 8
8
In a convex octagon, you can form triangles by selecting any three vertices. Since an octagon has 8 vertices, the number of ways to choose 3 vertices from these 8 is calculated using the combination formula ( \binom{n}{r} ), where ( n ) is the total number of vertices and ( r ) is the number of vertices to choose. Thus, the number of triangles formed is ( \binom{8}{3} = \frac{8!}{3!(8-3)!} = 56 ). Therefore, 56 triangles can be formed in an octagon.
In a polygon with ( n ) sides, the number of triangles that can be formed by connecting the vertices is given by the formula ( n - 2 ). For a 100-gon, this means you can create ( 100 - 2 = 98 ) triangles by connecting the vertices. Each triangle is formed by choosing any three of the 100 vertices.
30, its a combination. C(6,3) because there are six vertices of a hexagon and three vertices of a triangle