Christmas Cut-out

The original rectangle had a perimeter of $2 \times 30\text{cm} + 2\times 40\text{cm} = 140\text{cm}$.

Each of the new squares that is cut out adds three sides of $5\text{cm}$ each (shown in black on the diagram), and removes one portion of length $5\text{cm}$ (shown in green).

This means the overall effect of cutting out each square is to increase the perimeter by $10\text{cm}$. Since are ten squares, the overall increase is $10 \times 10 \text{cm} = 100\text{cm}$.

Therefore the final perimeter is $140\text{cm} + 100\text{cm} = 240\text{cm}$.