To solve the problem, let's analyze the image and the question it presents.

Problem Description:

The image shows a rectangle, and the problem asks for the value of the area of this rectangle. The dimensions provided are:

• Height ($h$) is $h = \frac{3}{2}x + 1$
• Width ($w$) is $x = 4$

Step-by-Step Solution:

1. Identify the height of the rectangle: The height is given as a function of $x$: $h = \frac{3}{2}x + 1$ Substituting $x = 4$ into this equation: $h = \frac{3}{2}(4) + 1 = 6 + 1 = 7$

2. Identify the width of the rectangle: The width is simply $x = 4$.

3. Calculate the area of the rectangle: The area $A$ of a rectangle is given by: $A = \text{height} \times \text{width}$ Substituting the values: $A = 7 \times 4 = 28$

So, the correct answer is $\boxed{28}$.

Multiple Choice Options:

Based on the provided multiple-choice answers, the correct answer is $A. 28$.

Do you need further details or have any questions?

Here are five related questions you might find interesting:

1. What is the derivative of the height function $h(x) = \frac{3}{2}x + 1$?
2. How would the area change if the value of $x$ were different?
3. Can you generalize the area function for any value of $x$?
4. What would the area be if $x = 5$?
5. How does the linearity of the height function affect the shape and area of the rectangle?

Tip: Always double-check your substitution to ensure the correct application of given values in a function.