Find the number of triangles and squares in the given figure.

The correct answer is Option (3) → 44 triangles, 10 squares

The figure is a big square cut into four small squares, each with both its diagonals drawn. The diagonals of the four small squares also join into the two diagonals of the big square and into a tilted square through the midpoints of its sides, so shapes are counted size by size.

Triangles:

• Smallest triangles, four in each small square: \(4\times4=16\)

• Half a small square (cut off by one diagonal), four in each small square: \(4\times4=16\)

• Triangles on each side of the big square with their tip at the centre (one quarter of the big square): 4

• Halves of the middle tilted square: 4

• Halves of the big square (cut off by a big diagonal): 4

• Total: \(16+16+4+4+4=44\)

Squares:

• The four small squares and the big square: 5

• The middle tilted square (green below) and the four small tilted squares inside it (shaded): 5

• Total: \(5+5=10\)