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What is the total area of the composite figure?

The given image shows a composite figure that consists of a rectangle and a semicircle. To find the total area of the figure, we need to calculate the areas of these two parts and then add them together.

1. **Rectangle**:
   - The width of the rectangle is given as 24 feet.
   - The height of the rectangle is 12 feet.
   
   The area of the rectangle (\(A_{\text{rectangle}}\)) is:
   \[
   A_{\text{rectangle}} = \text{width} \times \text{height} = 24 \, \text{ft} \times 12 \, \text{ft} = 288 \, \text{ft}^2
   \]

2. **Semicircle**:
   - The diameter of the semicircle is the same as the width of the rectangle, which is 24 feet. 
   - The radius of the semicircle (\(r\)) is half of the diameter:
   \[
   r = \frac{24}{2} = 12 \, \text{ft}
   \]
   The area of a full circle is given by \(A_{\text{circle}} = \pi r^2\). Since we are dealing with a semicircle, the area will be half of that:
   \[
   A_{\text{semicircle}} = \frac{1}{2} \times \pi r^2 = \frac{1}{2} \times \pi \times (12)^2 = 72\pi \, \text{ft}^2
   \]
   Approximating \(\pi \approx 3.1416\):
   \[
   A_{\text{semicircle}} \approx 72 \times 3.1416 = 226.195 \, \text{ft}^2
   \]

3. **Total Area**:
   The total area of the composite figure is the sum of the areas of the rectangle and the semicircle:
   \[
   A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 288 + 226.195 = 514.195 \, \text{ft}^2
   \]

So, the total area of the composite figure is approximately **514.2 square feet**.

Would you like further clarification or a breakdown of any step?

Here are 5 related questions to deepen your understanding:
1. How would the total area change if the height of the rectangle was doubled?
2. What would the area be if the semicircle was a full circle instead?
3. How would you calculate the perimeter of this composite figure?
4. What is the significance of using \(\pi\) in calculating the area of the semicircle?
5. How would the total area be affected if the diameter of the semicircle was reduced by half?

**Tip:** When dealing with composite figures, always break them into simpler geometric shapes, calculate each area, and sum them for the total.

Find the total area of a composite figure consisting of a rectangle and a semicircle. The rectangle has dimensions 24 feet by 12 feet, and the semicircle has a radius of 12 feet. This problem involves basic geometry concepts and area calculations, suitable for students in Grades 6-8.

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