Question

a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 32 ft long and 26 ft wide. find the area of the garden. use the value 3.14 for π, and do not round your answer. be sure to include the correct unit in your ans

Explanation:

Step1: Calculate area of rectangle

The area of a rectangle is given by the formula \( A_{rectangle} = length \times width \). Here, length is 32 ft and width is 26 ft.
\( A_{rectangle} = 32 \times 26 = 832 \) square feet.

Step2: Calculate area of semicircle

The diameter of the semicircle is equal to the width of the rectangle, which is 26 ft. So, the radius \( r = \frac{26}{2} = 13 \) ft.
The area of a full circle is \( A_{circle} = \pi r^2 \), so the area of a semicircle is \( A_{semicircle} = \frac{1}{2} \pi r^2 \).
Substituting \( \pi = 3.14 \) and \( r = 13 \):
\( A_{semicircle} = \frac{1}{2} \times 3.14 \times 13^2 \)
First, calculate \( 13^2 = 169 \).
Then, \( \frac{1}{2} \times 3.14 \times 169 = 1.57 \times 169 = 265.33 \) square feet.

Step3: Calculate total area of garden

The total area of the garden is the sum of the area of the rectangle and the area of the semicircle.
\( A_{total} = A_{rectangle} + A_{semicircle} = 832 + 265.33 = 1097.33 \) square feet.

Answer:

\( 1097.33 \) square feet (or \( 1097.33 \, \text{ft}^2 \))