The composite shape is a semicircle with a circle of radius Y removed from the centre. A- find an expression for the area of the semicircle. B- what is the seabed area of the composite shape? C- find the area of guarden (example as a garden with the shape) of x= 6m and Y = 0.5 m, correct to the nearest square m.

Let's break the problem into its parts to find the required areas for the composite shape, which consists of a semicircle with a smaller circle removed from the center.

### Part A: Find an expression for the area of the semicircle

The area \( A_{\text{semi}} \) of a semicircle with radius \( X \) is given by half the area of a full circle:
\[
A_{\text{semi}} = \frac{1}{2} \pi X^2
\]
where \( X \) is the radius of the semicircle.

### Part B: What is the area of the composite shape (the "seabed area")?

The composite shape has a semicircle of radius \( X \) with a circle of radius \( Y \) removed from its center. To find the seabed area, we subtract the area of the circle from the area of the semicircle.

The area of the circle to be removed is:
\[
A_{\text{circle}} = \pi Y^2
\]

Thus, the seabed area \( A_{\text{seabed}} \) is:
\[
A_{\text{seabed}} = A_{\text{semi}} - A_{\text{circle}} = \frac{1}{2} \pi X^2 - \pi Y^2
\]

### Part C: Calculate the area of the garden for \( X = 6 \, \text{m} \) and \( Y = 0.5 \, \text{m} \), correct to the nearest square meter.

1. **Area of the semicircle** with radius \( X = 6 \, \text{m} \):
\[
A_{\text{semi}} = \frac{1}{2} \pi (6)^2 = \frac{1}{2} \pi (36) = 18 \pi \approx 56.55 \, \text{m}^2
\]

2. **Area of the circle** with radius \( Y = 0.5 \, \text{m} \):
\[
A_{\text{circle}} = \pi (0.5)^2 = \pi (0.25) \approx 0.785 \, \text{m}^2
\]

3. **Seabed area**:
\[
A_{\text{seabed}} = 18 \pi - \pi (0.25) \approx 56.55 - 0.785 = 55.77 \, \text{m}^2
\]

To the nearest square meter, the seabed area is:
\[
A_{\text{seabed}} \approx 56 \, \text{m}^2
\]

### Final Answers:
- A) The area of the semicircle: \( A_{\text{semi}} = \frac{1}{2} \pi X^2 \)
- B) The seabed area: \( A_{\text{seabed}} = \frac{1}{2} \pi X^2 - \pi Y^2 \)
- C) The area of the garden when \( X = 6 \, \text{m} \) and \( Y = 0.5 \, \text{m} \) is approximately \( 56 \, \text{m}^2 \).

Would you like further details on any part of this solution?

### Related Questions:
1. How does the seabed area change if \( Y \) increases?
2. What is the perimeter of the composite shape?
3. What would be the area if \( X \) and \( Y \) were doubled?
4. How would the seabed area change if the circle were not centered?
5. What is the relationship between the semicircle’s radius and the area?

**Tip:** The area of composite shapes can always be found by adding and subtracting areas of simpler shapes.

The composite shape is a semicircle with a circle of radius Y removed from the centre. A- find an expression for the area of the semicircle. B- what is the seabed area of the composite shape? C- find the area of garden with the shape for X = 6m and Y = 0.5m, correct to the nearest square meter.

Learn how to find the area of a composite shape, which is a semicircle with a smaller circle removed from its center. This problem includes calculating the seabed area when X = 6m and Y = 0.5m, using geometry formulas. Suitable for Grades 6-8.

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