How many triangles can you count in the figure given ?
38
Let us begin by counting the smallest triangles assuming that they are 1 unit in side. You can find 12 triangles facing upwards (3 + 4 + 3 + 2) and 12 triangles facing downwards.
Now move to the bigger triangle with say side of 2 units. You can find 6 upward facing triangles (3 + 2 + 1) and 6 downward facing triangles.
Next are the biggest triangles with side 3 units (assumingly). You can find 1 upward facing triangle and 1 downward facing triangle.
12 + 12 + 6 + 6 + 1 + 1 = 38
