Find the number of triangles in the given figure.

Correct answer: 27

Count the triangles systematically by size so that no composite triangle is missed:

• 9 smallest single-region triangles.

• 9 triangles made by combining two small regions.

• 1 triangle made from four small regions.

• 4 triangles made from five small regions.

• 2 triangles made from six small regions.

• 2 largest composite triangles.

Total: 9 + 9 + 1 + 4 + 2 + 2 = 27.

This grouped counting method avoids both common errors: missing large composite triangles and double-counting overlapping regions.