4. A square with a side of 4 cm is divided into 16 squares with a side of $1 \mathrm{~cm}$, as shown in the diagram.

a) How many squares are there in the diagram?

b) Calculate the sum of the perimeters of all these

![](https://cdn.mathpix.com/cropped/2024_06_05_b088eb3db01806ad63fdg-02.jpg?height=214&width=242&top_left_y=1037&top_left_x=1244)
squares.
Solution. a) The drawing contains 16 squares with a side of $1 \mathrm{~cm}$, 9 squares with a side of $2 \mathrm{~cm}$, 4 squares with a side of $3 \mathrm{~cm}$, and 1 square with a side of $4 \mathrm{~cm}$. Therefore, the drawing contains $16+9+4+1=30$ squares.

b) The sum of the perimeters of all the squares in the given drawing is equal to:

$$
16 \cdot 4 \cdot 1+9 \cdot 4 \cdot 2+4 \cdot 4 \cdot 3+1 \cdot 4 \cdot 4=64+72+48+16=200 \mathrm{~cm}
$$

## VII Department