To find the area of the rose garden, we need to calculate the area of both the rectangle and the semicircle separately, then add them together.
1. Area of the rectangle:
Area = length * width
Area = 22 feet * 16 feet
Area = 352 square feet
2. Area of the semicircle:
The diameter of the semicircle is equal to the width of the rectangle, which is 16 feet.
Radius (r) = diameter / 2
= 16 feet / 2
= 8 feet
Area of semicircle = (π * r^2) / 2
= (π * 8^2) / 2
= (π * 64) / 2
= 32π square feet
Now, let's add the areas of the rectangle and semicircle:
Total area = Area of rectangle + Area of semicircle
= 352 square feet + 32π square feet
Rounding the final answer to the nearest hundredth:
Total area ≈ 352 + 32π square feet
≈ 352 + 100.53 square feet
≈ 452.53 square feet
Therefore, the area of the rose garden is approximately 452.53 square feet.
