21
depends on what shape that vertex is in
If all of the diagonals are drawn from a vertex of an octagon, how many triangles are formed
A heptagon has seven sides, so when drawing diagonals from one vertex, it will create five triangles. This is because each diagonal drawn from a single vertex will create a triangle until it intersects the previous diagonal. Therefore, the number of triangles formed by drawing all diagonals from one vertex in a heptagon is five.
The three major diagonals in an ordinary hexagon do not intersect at the same point. Therefore, in such a hexagon, the diagonals form 111 triangles.
1 triangle is formed.
Two triangles can be formed by the diagonals of one vertex of a four-sided polygon.
The number of triangles formed by the diagonals of a 21 sided polygon is C(21,3) = 21x20x19/3x2x1 = 1,330.
6
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).
There are 8
depends on what shape that vertex is in
98
98
It is: 8-2 = 6 triangles
how many triangles are formed when any parallelogram and it diagonals are drawn
In a 100-sided polygon, if diagonals are drawn from one vertex, they connect to all non-adjacent vertices. A vertex connects to 97 other vertices (100 total vertices minus the 1 vertex itself and the 2 adjacent vertices). The number of triangles formed with the diagonals from that vertex is given by the formula for combinations, specifically ( \binom{97}{2} ), which equals 4,656 triangles.
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.