Question

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a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 20 ft long and 14 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 formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 20\) ft and \(w=14\) ft.
\(A_{rectangle}=20\times14 = 280\) \(ft^{2}\)

Step2: Calculate the area of the semicircle

The formula for the area of a full - circle is \(A=\pi r^{2}\). For a semicircle, \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Given the diameter \(d = 14\) ft, so the radius \(r=\frac{d}{2}=\frac{14}{2}=7\) ft.
\(A_{semicircle}=\frac{1}{2}\times3.14\times7^{2}=\frac{1}{2}\times3.14\times49 = 76.93\) \(ft^{2}\)

Step3: Calculate the total area of the garden

The total area \(A = A_{rectangle}+A_{semicircle}\)
\(A=280 + 76.93=356.93\) \(ft^{2}\)

Answer:

\(356.93\) \(ft^{2}\)