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If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed?
n - 2
n - 1
n
n + 1
Solution:
We know that the number of triangles which are formed by connecting one of the vertices to the rest of the vertices is equal to n - 2.
For example,
For the quadrilateral, there are 4 sides
So we get 4 - 2 = 2
Here 2 triangles can be formed.
For a pentagon, there are 5 sides
So we get 5 - 2 = 3
Here 3 triangles can be formed.
Therefore, n - 2 triangles are formed.
If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed?
Summary:
If all of the diagonals are drawn from a vertex of an n-gon, n - 2 triangles are formed.
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