https://file.aiquickdraw.com/mathbot/file/1727930788921a2ghvf52.jpg

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.

Find the area of the shape with the indicated dimensions. Use π = 3.14. Round your answer to the nearest hundredth.

Learn how to calculate the area of a composite figure consisting of a rectangle and a semicircle. Dimensions provided: height of the rectangle is 8.46 ft and the width (also the diameter of the semicircle) is 6.12 ft. The solution includes detailed steps and the use of π = 3.14, rounded to the nearest hundredth. Suitable for students in Grades 6-8.

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