To calculate the total perimeter of the figure:

1. Identify all straight-line segments and their lengths:

   • The horizontal straight-line segment at the top is 4 cm (given).
   • The vertical straight-line segment on the left is also 4 cm (since the grid is uniform and each square is 4 cm by 4 cm).

2. Identify curved parts:

   • Each curved part is a quarter-circle.
   • Since there are two quarter-circles, combined they form a half-circle.
   • The radius of each quarter-circle is 4 cm (as each grid square is 4 cm wide).

3. Calculate the total perimeter:

   • Straight segments: $4 + 4 = 8 \, \text{cm}$.
   • Half-circle perimeter: $\text{Circumference of a full circle} = 2\pi \times \text{radius} = 2\pi \times 4 = 8\pi \, \text{cm}.$ Half-circle circumference: $\frac{8\pi}{2} = 4\pi \, \text{cm}.$

4. Add everything together: $\text{Total perimeter} = 8 + 4\pi \, \text{cm}.$

For simplicity, if you need a decimal approximation:

• $4\pi \approx 12.57 \, \text{cm}$,
• Total perimeter $\approx 8 + 12.57 = 20.57 \, \text{cm}$.

Final Answer: $8 + 4\pi \, \text{cm}$ or approximately $20.57 \, \text{cm}$.

Would you like a further breakdown or have any questions?

Related Questions:

1. What is the total area of this figure?
2. How would the perimeter change if the radius were doubled?
3. What is the length of the curved parts combined in terms of their degrees?
4. How does the use of $\pi$ simplify calculations for circles?
5. What would the total perimeter be if the grid square was 5 cm instead of 4 cm?

Tip: Always visualize breaking complex shapes into simple components for easier calculations.