Calculating Area of a Rose Garden
To find the area of this rose garden, you need to calculate the area of the rectangle and add the areas of the two semi-circles on either end of the rectangle.
First, calculate the area of the rectangle. The area \( A_{rectangle} \) is given by the formula:
\[ A_{rectangle} = \text{length} \times \text{width} \]
For this garden:
\[ A_{rectangle} = 21 \text{ ft} \times 14 \text{ ft} = 294 \text{ ft}^2 \]
Now calculate the area of a full circle and then take half of it to get the area of a semi-circle. The diameter of the circles is the width of the rectangle, which is 14 feet. The radius \( r \) is therefore 7 feet (since radius is half the diameter). The area \( A_{circle} \) of a full circle is given by the formula:
\[ A_{circle} = \pi r^2 \]
But since we have two semi-circles, their combined area will equal the area of one full circle. So we will use the formula for a full circle and not divide it by 2 in the end. Let's calculate this area using \( \pi \approx 3.14 \):
\[ A_{circle} = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \text{ ft}^2 \]
So, to find the total area of the garden \( A_{garden} \), add the area of the rectangle and the area of the circles:
\[ A_{garden} = A_{rectangle} + A_{circle} \]
\[ A_{garden} = 294 \text{ ft}^2 + 153.86 \text{ ft}^2 = 447.86 \text{ ft}^2 \]
Now, round to the nearest whole number if necessary and do not round your answer:
\[ A_{garden} \approx 448 \text{ ft}^2 \]
Therefore, the area of the garden is approximately 448 square feet.
