To find the area of the given shape, we need to break it down into smaller, familiar geometric shapes like rectangles and triangles.

Step 1: Identify Sub-shapes

The diagram appears to be a rectangular area with two cut-outs:

1. Top-left cut-out: A rectangle measuring $3.9 \, \text{mm} \times 4 \, \text{mm}$.
2. Bottom-left cut-out: A right triangle with legs of $4 \, \text{mm}$ and $6.7 \, \text{mm}$.

The remaining shape resembles a larger rectangle with dimensions $11 \, \text{mm} \times 7.5 \, \text{mm}$, from which the cut-out areas need to be subtracted.

Step 2: Calculate Areas of Shapes

1. Area of the larger rectangle:
   $A_1 = 11 \, \text{mm} \times 7.5 \, \text{mm} = 82.5 \, \text{mm}^2$

2. Area of the top-left cut-out rectangle:
   $A_2 = 3.9 \, \text{mm} \times 4 \, \text{mm} = 15.6 \, \text{mm}^2$

3. Area of the bottom-left triangle:
   $A_3 = \frac{1}{2} \times 4 \, \text{mm} \times 6.7 \, \text{mm} = 13.4 \, \text{mm}^2$

Step 3: Subtract the Cut-outs from the Large Rectangle

$\text{Total Area} = A_1 - A_2 - A_3$ $\text{Total Area} = 82.5 \, \text{mm}^2 - 15.6 \, \text{mm}^2 - 13.4 \, \text{mm}^2$ $\text{Total Area} = 53.5 \, \text{mm}^2$

Final Answer

The area of the shape is: $\boxed{53.5 \, \text{mm}^2}$

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How do you find the area of complex shapes?
2. What are some strategies for decomposing irregular shapes?
3. Why is the formula for the area of a triangle $\frac{1}{2} \times \text{base} \times \text{height}$?
4. How does changing the dimensions affect the total area?
5. What are the units of area, and why are they squared?

Tip: When working with irregular shapes, dividing them into familiar geometric shapes helps simplify calculations!