The shape you have uploaded is a composite geometric figure. To find its area, we need to break it down into simpler shapes like rectangles and triangles. Here's the step-by-step breakdown:

Step 1: Split the shape

• The shape consists of:
  1. A large rectangle with dimensions $4.3 \, \text{mm} \times 9.1 \, \text{mm}$
  2. A right triangle with a base of $8 \, \text{mm}$ and height of $2 \, \text{mm}$

Step 2: Calculate the area of the large rectangle

The formula for the area of a rectangle is: $\text{Area}_{\text{rectangle}} = \text{length} \times \text{width}$ For the rectangle: $\text{Area}_{\text{rectangle}} = 4.3 \, \text{mm} \times 9.1 \, \text{mm} = 39.13 \, \text{mm}^2$

Step 3: Calculate the area of the right triangle

The formula for the area of a triangle is: $\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$ For the triangle: $\text{Area}_{\text{triangle}} = \frac{1}{2} \times 8 \, \text{mm} \times 2 \, \text{mm} = 8 \, \text{mm}^2$

Step 4: Add the areas

Now, sum the areas of the rectangle and the triangle: $\text{Total Area} = 39.13 \, \text{mm}^2 + 8 \, \text{mm}^2 = 47.13 \, \text{mm}^2$

Final Answer:

The area of the shape is 47.13 mm².

Would you like a more detailed breakdown of any step, or do you have any questions?

Here are five related questions you can explore:

1. How do you find the perimeter of this composite shape?
2. What happens if the base of the triangle changes—how would that affect the area?
3. How would you calculate the area if one of the dimensions were missing?
4. How does the concept of decomposition help in solving complex area problems?
5. What other types of composite shapes can you break down using basic geometric shapes?

Tip: When dealing with composite shapes, always break them down into familiar simple shapes like triangles and rectangles for easier calculations.