The problem involves calculating the perimeter of the shaded shape formed by three identical right-angled triangles and a square. Here's the step-by-step solution:

Step 1: Analyzing the Shape

1. The shape includes:
   • A square with side length 9.6 cm (as labeled in the image).
   • Three identical right-angled triangles, each with:
     • Hypotenuse = 16 cm (given).
     • Base = 9.6 cm (the same as the square's side length).
     • Height = 12.8 cm (given in the diagram).

Step 2: Perimeter of the Shaded Shape

To calculate the perimeter, sum the lengths of all the outer edges of the shaded shape.

Outer edges:

1. Hypotenuse of Triangle 1 = $16 \, \text{cm}$.
2. Hypotenuse of Triangle 2 = $16 \, \text{cm}$.
3. Hypotenuse of Triangle 3 = $16 \, \text{cm}$.
4. Side of the square (shared by the shaded shape) = $9.6 \, \text{cm}$.
5. Vertical height (12.8 cm) appears as the rightmost side.

Total Perimeter

$\text{Perimeter} = 16 + 16 + 16 + 9.6 + 12.8$

$\text{Perimeter} = 70.4 \, \text{cm}$

Final Answer:

The perimeter of the shaded shape is: $\boxed{70.4 \, \text{cm}}$

Would you like further clarification or a breakdown of any specific part?

Related Questions:

1. How is the Pythagorean theorem applied to confirm the triangle dimensions?
2. What is the total area of the shaded shape?
3. How would the perimeter change if one of the triangles was removed?
4. Can this shape be simplified further for a different calculation?
5. What are practical applications of calculating perimeters in geometry?

Tip:

When working with composite shapes, carefully identify and trace all outer edges to avoid missing sections of the perimeter.