Question

how many squares are in this picture?

Explanation:

Step1: Count small squares

Count the smallest - sized squares. There are \(4\times4 = 16\) small squares in the large \(4\times4\) grid and \(2\times2=4\) small squares in the two \(2\times2\) sub - grids. So, \(16 + 4=20\) small squares.

Step2: Count larger squares

Count \(2\times2\) squares in the large grid. There are \(3\times3 = 9\) \(2\times2\) squares in the \(4\times4\) grid.
Count \(3\times3\) squares in the large grid. There are \(2\times2=4\) \(3\times3\) squares in the \(4\times4\) grid.
Count the \(4\times4\) square (1 square).

Step3: Sum up

The total number of squares is \(20+9 + 4+1=34\).

Answer:

34