https://file.aiquickdraw.com/mathbot/file/1725370395088s8g8fdd9.jpg

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.

What is the area of the rectangle? The area is found by multiplying the height and width of the rectangle.

Learn how to calculate the area of a rectangle using its height and width. In this problem, the height is a linear function of x, and the width is a constant value. This example is suitable for students in Grades 6-8.

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