Let's analyze the problem presented in the image:

Problem Overview:

1. Two identical rectangles (ABCD and WXYZ) overlap, forming a figure with 5 shaded squares.
2. The total area of the 5 shaded squares is given as 245 cm².
3. Part (a) asks for the length of one side of a shaded square.
4. Part (b) asks for the total area of the entire figure.

Solution Approach:

(a) Finding the length of one side of a shaded square:

1. Let $s$ be the side length of one shaded square.
2. The area of one shaded square is $s^2$.
3. Since there are 5 identical shaded squares, the total shaded area is: $5 \times s^2 = 245 \, \text{cm}^2$
4. Solving for $s$: $s^2 = \frac{245}{5} = 49$ $s = \sqrt{49} = 7 \, \text{cm}$ Thus, the length of one side of a shaded square is 7 cm.

(b) Finding the total area of the figure:

1. Since the rectangles are identical, we need to find the area of one rectangle.
2. Let $l$ and $w$ be the length and width of each rectangle. We also know the width is $s = 7 \, \text{cm}$ (from the length of the square's side).
3. To determine $l$:
   • Use the relationship between the rectangles and the number of squares to deduce the length.
   • However, since part (b) is a continuation of the problem, additional information about the overlap between the rectangles may be needed to finalize this calculation.

Would you like further details on how to solve for the total area or any other aspects of this problem? Here are some related questions that might help:

1. How do you calculate the total area when two identical figures overlap?
2. What formula relates the area of a rectangle to its length and width?
3. How can you verify the correctness of the side length of the shaded square?
4. What steps are necessary to calculate the area of overlapping shapes?
5. How can you visualize the overlap of shapes to better understand area calculations?

Tip: Always ensure you understand the relationships between overlapping shapes and the dimensions involved to avoid mistakes in area calculations.