Many people asked me to find an solution to the questions like find the Number of Triangles within a triangle.
I researched a lot to find the solution of this Problem and found the following Data:
b n
1 1
2 5
3 13
4 27
5 48
6 78
7 118
8 170
Where b= No. of Triangles in any base of the equilateral triangle. and n= No. of Triangles contain in the given triangle. But this procedure is very difficult to memorize each of the triangle for each of the given triangle.
Formula for Determining the No.of Triangles:
A simplified formula for determining no. of triangles = n*(n+2)*(2n+1)/8
where n= No. of Triangles on each base 
For the given problem on the picture Find the No. of triangles… No. of Triangles in the above picture = 6*(6+2)*(12+1)/8 =78 triangles. Hope this small trick will work for the learners.
