To solve this problem, let's calculate the shaded area step-by-step:

Step 1: Understand the problem

• Each rectangle has dimensions:
  • Length = 7 cm
  • Width = 0.5 cm
• Four rectangles are placed to form a larger figure.
• The shaded area is the central part, formed by subtracting the areas of the outer unshaded rectangles from the area of the larger rectangle.

Step 2: Dimensions of the larger rectangle

The larger rectangle is made by aligning four rectangles:

• The width of the larger rectangle is the length of one rectangle = 7 cm.
• The height of the larger rectangle is the sum of two widths (0.5 cm each) = 2 × 0.5 cm = 1 cm.

Thus, the dimensions of the larger rectangle are:

• Length = 7 cm
• Height = 1 cm

The area of the larger rectangle is: $\text{Area} = \text{Length} \times \text{Height} = 7 \, \text{cm} \times 1 \, \text{cm} = 7 \, \text{cm}^2$

Step 3: Dimensions of the unshaded rectangles

The unshaded area is formed by removing four smaller rectangles from the larger rectangle:

• Two smaller rectangles on the sides:

  • Dimensions: $7 \, \text{cm} \times 0.5 \, \text{cm}$
  • Area of one = $7 \times 0.5 = 3.5 \, \text{cm}^2$
  • Total area of the two side rectangles = $2 \times 3.5 = 7 \, \text{cm}^2$

• Two smaller rectangles on the top and bottom:

  • Dimensions: $0.5 \, \text{cm} \times 0.5 \, \text{cm}$
  • Area of one = $0.5 \times 0.5 = 0.25 \, \text{cm}^2$
  • Total area of the two top and bottom rectangles = $2 \times 0.25 = 0.5 \, \text{cm}^2$

Total unshaded area = $7 + 0.5 = 7.5 \, \text{cm}^2$.

Step 4: Shaded area

The shaded area is the area of the larger rectangle minus the unshaded area: $\text{Shaded Area} = \text{Area of Larger Rectangle} - \text{Unshaded Area}$ $\text{Shaded Area} = 7 - 7.5 = -0.5 \, \text{cm}^2$

It seems there might be a mistake in dimensions or interpretation. Could you confirm the exact structure of the shaded part? Let me know, and I’ll adjust the solution accordingly.

Would you like me to refine or explain this further? Let me know!

Here are 5 questions that could expand your understanding:

1. What formula is used to calculate the area of a rectangle?
2. How is the total area of combined rectangles determined?
3. What are common errors when calculating the shaded region?
4. How could you verify the solution for such problems?
5. How does scaling dimensions affect the total area?

Tip: Double-check dimensions and ensure all subtracted areas are included to avoid errors.