https://file.aiquickdraw.com/mathbot/file/1729859953915g3tnavbb.jpg

Let's break down the figure, which consists of a rectangle and a semicircle.

1. **Rectangle**:
   - Length = 25 inches
   - Width = 16 inches
   - The area of a rectangle is calculated using the formula:
     \[
     A_{\text{rectangle}} = \text{length} \times \text{width} = 25 \times 16 = 400 \, \text{square inches}
     \]

2. **Semicircle**:
   - The diameter of the semicircle is equal to the width of the rectangle, which is 16 inches. Thus, the radius \( r \) of the semicircle is:
     \[
     r = \frac{16}{2} = 8 \, \text{inches}
     \]
   - The area of a full circle is given by \( A_{\text{circle}} = \pi r^2 \), so for a semicircle, the area is half of that:
     \[
     A_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (8^2) = \frac{1}{2} \pi (64) = 32\pi \, \text{square inches}
     \]

3. **Total area**:
   The total area of the figure is the sum of the areas of the rectangle and the semicircle:
   \[
   A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 400 + 32\pi
   \]

Thus, the correct answer is:
\[
\boxed{400 + 32\pi}
\]

Let me know if you need further details or explanations.

Here are five related questions for practice:
1. How would the total area change if the diameter of the semicircle were doubled?
2. What would be the perimeter of this figure?
3. How does the area of a quarter circle compare to that of a semicircle?
4. What is the area of a rectangle with a length of 50 inches and a width of 16 inches?
5. How would you calculate the area if the shape were a quarter circle instead of a semicircle?

**Tip:** Always double-check whether the shape in question is a full, half, or quarter of a circle when dealing with composite figures involving circles.

This figure consists of a rectangle and a semicircle. What is the area, in square inches, of this figure?

Learn how to calculate the area of a composite figure consisting of a rectangle and a semicircle. This problem involves calculating the areas of both shapes and adding them together. Suitable for students in Grades 8-10.

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