Final answer:
To calculate the area of the rose garden, find the areas of both the rectangle and the semicircle using the dimensions provided and add them together. The total area without rounding is 995.94 ft², which corresponds to option d) 1008 ft².
Step-by-step explanation:
The question involves a rose garden that combines both a rectangle and a semicircle. To find the total area of the garden, you need to calculate the area of the rectangle and the area of the semicircle using the dimensions provided. The rectangle is 28 ft long and 22 ft wide.
Firstly, calculate the area of the rectangle by multiplying the length by the width:
- Arearectangle = Length × Width = 28 ft × 22 ft = 616 ft².
Next, we calculate the area of the semicircle. The diameter of the semicircle is the same as the width of the rectangle, which is 22 ft. Therefore, the radius (r) of the semicircle is 22 ft / 2 = 11 ft. Now apply the formula for the area of a semicircle, which is half the area of a full circle, πr² / 2.
- Areasemicircle = (π × r²) / 2 = (3.14 × 11 ft × 11 ft) / 2 = (3.14 × 121 ft²) / 2 = 379.94 ft².
Now, add the areas of the rectangle and the semicircle to find the total area of the garden:
- Total area = Arearectangle + Areasemicircle = 616 ft² + 379.94 ft² = 995.94 ft².
As the answer should not be rounded, the final answer is 995.94 ft², which is closest to option d) 1008 ft² when not rounding.