To find the area of the piecewise rectangular figure, we can break the shape into smaller, more manageable rectangles. Let's divide the given figure into three rectangular sections.

Step 1: Identify the three rectangles

• Bottom rectangle: Width = 5 in, Height = 5 in
• Middle rectangle: Width = 4 in, Height = 3 in
• Top rectangle: Width = 4 in, Height = 2 in

Step 2: Calculate the area of each rectangle

• Area of the bottom rectangle: $5 \text{ in} \times 5 \text{ in} = 25 \text{ square inches}$
• Area of the middle rectangle: $4 \text{ in} \times 3 \text{ in} = 12 \text{ square inches}$
• Area of the top rectangle: $4 \text{ in} \times 2 \text{ in} = 8 \text{ square inches}$

Step 3: Sum the areas

$\text{Total Area} = 25 + 12 + 8 = 45 \text{ square inches}$

So, the area of the piecewise rectangular figure is 45 square inches.

Do you want any further details or clarifications?

Here are some related questions you can explore:

1. How would you find the perimeter of this figure?
2. Can this shape be divided differently for calculating the area?
3. What if one of the lengths was missing? How would you calculate it?
4. How does this method work for more complex shapes?
5. What is the difference between calculating area and perimeter for irregular figures?

Tip:

When dealing with composite shapes, breaking them down into simpler shapes like rectangles or triangles often simplifies the calculations.