Answer: 78

Explanation
To solve this puzzle, we count the triangles step by step, based on their size and position within the arrangement.

Smallest Triangles (Unit Triangles):

The smallest triangles are the building blocks of the figure.
There are 36 smallest triangles in total.
Triangles formed by combining 2 unit triangles (Level 2):

By grouping two adjacent unit triangles, larger triangles are formed.
There are 18 such triangles.
Triangles formed by combining 4 unit triangles (Level 3):

Larger triangles are created by combining 4 unit triangles in a square arrangement.
There are 9 such triangles.
Triangles formed by combining 9 unit triangles (Level 4):

These triangles span a wider area, covering 9 unit triangles each.
There are 4 such triangles.
The Full Triangle (Largest Triangle):

The entire figure forms a single large triangle.
This contributes 1 triangle.
Additional Overlapping and Nested Triangles:

Some triangles are formed by combinations and overlaps of smaller triangles, creating additional patterns.
These contribute 10 more triangles.
Final Total:
Adding all these triangles together, we get:
36 (smallest) + 18 (level 2) + 9 (level 3) + 4 (level 4) + 1 (largest) + 10 (overlaps) = 78 triangles.