The image shows a composite figure that consists of a rectangle and a semicircle on top. The dimensions provided are:

• Height of the rectangle: $8.46 \, \text{ft}$
• Width of the rectangle (and the diameter of the semicircle): $6.12 \, \text{ft}$

To find the area of this figure, we need to calculate:

1. Area of the rectangle:
   $A_{\text{rectangle}} = \text{height} \times \text{width} = 8.46 \times 6.12$

2. Area of the semicircle: The radius of the semicircle is half of the diameter:
   $r = \frac{6.12}{2} = 3.06 \, \text{ft}$

   The area of a full circle is $\pi r^2$, so the area of the semicircle is:
   $A_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times (3.06)^2$

Finally, add the areas of the rectangle and the semicircle together to get the total area of the shape.

Let me calculate that for you.

1. Area of the rectangle:
   $A_{\text{rectangle}} = 8.46 \times 6.12 = 51.7272 \, \text{ft}^2$

2. Area of the semicircle:
   $A_{\text{semicircle}} = \frac{1}{2} \times 3.14 \times (3.06)^2 = \frac{1}{2} \times 3.14 \times 9.3636 = 14.702 \, \text{ft}^2$

3. Total area:
   $A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 51.7272 + 14.702 = 66.4292 \, \text{ft}^2$

Rounding to the nearest hundredth, the total area is approximately 66.43 square feet.

Would you like more details or have any questions about this calculation?

Here are 5 related questions to explore further:

1. How would the area change if the semicircle was a full circle instead?
2. What is the perimeter of this figure?
3. How does the area change if the diameter of the semicircle doubles?
4. What is the area if we use a more accurate value of $\pi$, such as 3.14159?
5. How do we find the volume if this figure were a 3D object with a given thickness?

Tip: For composite figures, always break the shape into simpler geometric shapes to calculate areas more easily.