Solution

To solve this, we need to systematically count all the squares and triangles in the figure.

1. Counting the Squares

• Small squares: There are 4 small squares forming the main body.
• Medium square: The 4 small squares combine to form 1 larger square.
• Tilted square: There is 1 square in the center, tilted on its corner.

Total Squares = 4 + 1 + 1 = 6 squares.

2. Counting the Triangles

We can count the triangles by grouping them based on the number of small triangular units they contain.

• Triangles made of 1 unit: There are 16 such triangles.
• Triangles made of 2 units: There are 8 such triangles.
• Triangles made of 4 units: There are 4 such triangles (the four main quadrants of the large square).

Total Triangles = 16 + 8 + 4 = 28 triangles.

Conclusion:

The figure contains 28 triangles and 6 squares.