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.

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