To find the area of the figure, we need to calculate the area of both the rectangle and the semicircle separately, then add them together.

Step 1: Calculate the Area of the Rectangle

The rectangle has a length of 6 and a width of 4. The area of a rectangle is given by: $\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 6 \times 4 = 24$

Step 2: Calculate the Area of the Semicircle

The semicircle has a diameter of 4 (the same as the width of the rectangle), so its radius $r$ is: $r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2$

The area of a full circle is given by: $\text{Area}_{\text{circle}} = \pi r^2$ For a semicircle, we take half of that: $\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2)^2 = \frac{1}{2} \pi \times 4 = 2\pi$

Using an approximate value of $\pi \approx 3.14$: $\text{Area}_{\text{semicircle}} \approx 2 \times 3.14 = 6.28$

Step 3: Add the Areas Together

Now, we add the area of the rectangle and the area of the semicircle: $\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}} = 24 + 6.28 = 30.3$

Final Answer (rounded to the nearest tenth):

$\text{Total Area} \approx 30.3 \text{ square units}$

Would you like further details on this solution or have any questions?

Here are five related questions to expand on this topic:

1. How would the area change if the diameter of the semicircle was doubled?
2. What if the rectangle’s length was increased to 8? How would that impact the total area?
3. How would you find the perimeter of this composite shape?
4. If the semicircle were a full circle instead, how would you calculate the total area?
5. How can we find the area of similar composite shapes with different polygons and circles?

Tip: Remember, for composite shapes, break them down into simple shapes, calculate each area, and then add them up.