To find the area of the shaded part of the rectangle, we'll need to calculate the area of the rectangle and then subtract the area of the unshaded triangle.

1. Calculate the area of the rectangle: $\text{Area of rectangle} = \text{length} \times \text{width} = 19 \text{ in} \times 16 \text{ in} = 304 \text{ in}^2$

2. Calculate the area of the unshaded triangle: The base of the triangle is the same as the width of the rectangle, which is 19 inches. The height of the triangle is the difference between the height of the rectangle and the vertical height of the shaded part, which is $16 \text{ in} - 7 \text{ in} = 9 \text{ in}$.

   $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 19 \text{ in} \times 9 \text{ in} = \frac{1}{2} \times 171 \text{ in}^2 = 85.5 \text{ in}^2$

3. Calculate the area of the shaded part: $\text{Area of shaded part} = \text{Area of rectangle} - \text{Area of triangle} = 304 \text{ in}^2 - 85.5 \text{ in}^2 = 218.5 \text{ in}^2$

Thus, the area of the shaded part of the rectangle is $218.5 \text{ in}^2$.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How do you find the area of a parallelogram?
2. What is the formula for the area of a trapezoid?
3. How can you determine the area of a complex shape by dividing it into simpler shapes?
4. What is the significance of understanding areas in real-world applications?
5. How do you find the perimeter of the shaded part of the rectangle?

Tip: When solving geometry problems involving composite shapes, always identify and calculate the areas of the simpler shapes first, then combine them as needed.