https://file.aiquickdraw.com/mathbot/file/17297250270654emyk93m.jpg

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:
\[
\boxed{53.5 \, \text{mm}^2}
\]

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Would you like further details or have any questions?

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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!

Find the area of the given shape using the provided dimensions.

Calculate the area of a complex shape with cut-outs by breaking it into simpler shapes. Learn how to subtract the area of a rectangle and a triangle from the larger rectangle. Suitable for Grades 6-8 students, with a detailed solution.

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