Question

a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 32 ft long and 24 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 answer.

Explanation:

Step1: Calculate the area of the rectangle

The area formula for a rectangle is \(A_{rectangle}=l\times w\). Given \(l = 32\) ft and \(w = 24\) ft.
\(A_{rectangle}=32\times24=768\) square - feet.

Step2: Calculate the area of the semicircle

The diameter of the semicircle \(d = 24\) ft, so the radius \(r=\frac{d}{2}=\frac{24}{2}=12\) ft.
The area formula for a semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Substitute \(\pi = 3.14\) and \(r = 12\) ft.
\(A_{semicircle}=\frac{1}{2}\times3.14\times12^{2}=\frac{1}{2}\times3.14\times144 = 226.08\) square - feet.

Step3: Calculate the total area of the garden

The total area \(A = A_{rectangle}+A_{semicircle}\).
\(A=768 + 226.08=994.08\) square - feet.

Answer:

\(994.08\) square - feet