https://file.aiquickdraw.com/mathbot/file/172982622890262ioc0b1.jpg

In this image, the problem involves calculating the area of a composite shape, which consists of a rectangle and a semicircle. Here's a step-by-step breakdown:

1. **Identify the shapes:**
   - The composite shape consists of a **rectangle** and a **semicircle**.
   
2. **Formulas to use:**
   - **Area of a rectangle:** \( A_{\text{rect}} = L \times W \)
   - **Area of a semicircle:** \( A_{\text{semi}} = \frac{\pi r^2}{2} \), where \( r \) is the radius.

3. **Measurements from the diagram:**
   - **Rectangle dimensions:** 
     - Length = 48.0 ft
     - Width = 50.0 ft
   - **Semicircle radius:**  The width of the rectangle is 50.0 ft, and the semicircle is attached to the shorter side, so the **radius is half of 15.0 ft**: \( r = \frac{15.0}{2} = 7.5 \, \text{ft} \).

4. **Calculation steps:**
   - **Area of the rectangle:** 
     \[
     A_{\text{rect}} = 48.0 \, \text{ft} \times 50.0 \, \text{ft} = 2400 \, \text{ft}^2
     \]
   - **Area of the semicircle:**
     \[
     A_{\text{semi}} = \frac{\pi \times (7.5 \, \text{ft})^2}{2} = \frac{\pi \times 56.25}{2} = 88.36 \, \text{ft}^2
     \]
   
5. **Total area:**
   - Sum the two areas:
     \[
     A_{\text{total}} = 2400 \, \text{ft}^2 + 88.36 \, \text{ft}^2 = 2488.36 \, \text{ft}^2
     \]
   - Rounding to significant digits (based on the precision in the given measurements):
     \[
     A_{\text{total}} \approx 2490 \, \text{ft}^2
     \]

Let me know if you'd like further clarifications or additional details!

Here are 5 related questions to deepen understanding:
1. How would the total area change if the radius of the semicircle doubled?
2. How do you determine the number of significant digits in your final answer?
3. What is the difference in area if the semicircle was a full circle instead?
4. How would the area be affected if the rectangle was a square with sides of 50 ft?
5. What is the formula for calculating the perimeter of this composite shape?

**Tip:** Always ensure your significant figures match the precision of the given measurements to avoid overestimating accuracy.

The goal here is to calculate the area of a compound shape consisting of a rectangle and a semicircle. The rectangle has dimensions of 48 ft by 50 ft, and the semicircle is attached to the shorter side with a radius of 7.5 ft.

Learn how to calculate the area of a composite shape consisting of a rectangle (48 ft by 50 ft) and a semicircle with a radius of 7.5 ft. The solution uses geometry formulas and considers significant digits in the final answer. Suitable for students in Grades 7-10.

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