To determine the area of this shape, we must break it into simpler components. This composite figure consists of:

1. A rectangle: Dimensions are $4 \, \text{m} \times 6 \, \text{m}$.
2. A semicircle: Diameter is $4 \, \text{m}$, so the radius is $2 \, \text{m}$.
3. A right triangle: Base is $7 \, \text{m}$ and height is $2 \, \text{m}$.

Calculations:

1. Area of the rectangle: $\text{Area} = \text{length} \times \text{width} = 4 \times 6 = 24 \, \text{m}^2$

2. Area of the semicircle: $\text{Area} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2^2) = \frac{1}{2} \pi (4) = 2\pi \, \text{m}^2$ Using $\pi \approx 3.14$: $\text{Area} \approx 2 \times 3.14 = 6.28 \, \text{m}^2$

3. Area of the triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 2 = 7 \, \text{m}^2$

4. Total Area: Adding these together: $\text{Total Area} = \text{Area of rectangle} + \text{Area of semicircle} + \text{Area of triangle}$ $\text{Total Area} = 24 + 6.28 + 7 = 37.28 \, \text{m}^2$

Final Answer:

The total area of the shape is approximately: $\boxed{37.28 \, \text{m}^2}$

Let me know if you want detailed steps for a specific part!
Here are some related questions to consider:

1. How would the total area change if the semicircle were a full circle?
2. What is the perimeter of the given shape?
3. How would you compute the area if the dimensions were doubled?
4. Can this shape be divided differently to simplify calculations?
5. What happens to the semicircle’s area if the radius is halved?

Tip: Always double-check the units in your calculations to ensure they are consistent throughout!