To solve the problem, we need to find the area of the shaded region by subtracting the area of the smaller rectangle (inner rectangle) from the area of the larger rectangle (outer rectangle).

Step 1: Area of the larger rectangle

The larger rectangle has dimensions:

• Width = 19 inches
• Height = 11 inches

The area is calculated as: $\text{Area of larger rectangle} = \text{Width} \times \text{Height} = 19 \times 11 = 209 \, \text{square inches.}$

Step 2: Area of the smaller rectangle

The smaller rectangle has dimensions:

• Width = 15 inches
• Height = 7 inches

The area is calculated as: $\text{Area of smaller rectangle} = \text{Width} \times \text{Height} = 15 \times 7 = 105 \, \text{square inches.}$

Step 3: Area of the shaded region

To find the shaded region's area, subtract the area of the smaller rectangle from the area of the larger rectangle: $\text{Area of shaded region} = \text{Area of larger rectangle} - \text{Area of smaller rectangle} = 209 - 105 = 104 \, \text{square inches.}$

Final Answer:

The area of the shaded region is 104 square inches.

Do you want a detailed explanation for any step or related concepts? Here are some follow-up questions to expand your understanding:

1. How is the area of a rectangle calculated for more complex problems?
2. What happens when the shapes are irregular instead of rectangles?
3. Can you find the perimeter of the shaded region?
4. How would this change if the dimensions of one rectangle were doubled?
5. What is the significance of subtracting areas in solving composite shape problems?

Tip: Always label dimensions clearly and double-check subtraction for composite shapes to avoid errors.