https://file.aiquickdraw.com/mathbot/file/1732552548283fdbu8rxz.jpg

To find the area of the figure, which consists of a rectangle and a semicircle, we can calculate their areas separately and then sum them up.

### 1. Area of the rectangle:
The formula for the area of a rectangle is:
\[
\text{Area of rectangle} = \text{length} \times \text{width}
\]
From the diagram:
- Length = \(14\)
- Width = Radius of the semicircle = \(3\)

\[
\text{Area of rectangle} = 14 \times 3 = 42
\]

### 2. Area of the semicircle:
The formula for the area of a circle is:
\[
\text{Area of circle} = \pi r^2
\]
For a semicircle, divide by 2:
\[
\text{Area of semicircle} = \frac{\pi r^2}{2}
\]
Given \(r = 3\):
\[
\text{Area of semicircle} = \frac{\pi (3^2)}{2} = \frac{\pi (9)}{2} = \frac{9\pi}{2} \approx \frac{28.274}{2} \approx 14.1
\]

### 3. Total area:
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of semicircle}
\]
\[
\text{Total area} = 42 + 14.1 = 56.1
\]

### Final Answer:
The total area is approximately **56.1 square units**.

Would you like further clarifications or have more questions? Here are some related questions:

1. How is the area of a semicircle derived from a full circle?
2. Why is the width of the rectangle equal to the radius of the semicircle?
3. Can this method be extended to figures combining other geometric shapes?
4. What happens if the dimensions of the figure are doubled? How does the area change?
5. How can we verify the result using approximation techniques?

**Tip:** Always double-check units when working with composite shapes to ensure consistency in calculations.

Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenths place.

Learn how to calculate the area of a composite figure made up of a rectangle and a semicircle. Includes step-by-step solutions using geometry formulas. Suitable for students in Grades 6-8.

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