Question

a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 33 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 answer.
26 ft
33 ft

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=length\times width\).
Given \(length = 33\) ft and \(width=26\) ft, so \(A_{rectangle}=33\times26 = 858\) \(ft^{2}\).

Step2: Calculate the area of the semicircle

The diameter of the semicircle is equal to the width of the rectangle, so \(d = 26\) ft, and the radius \(r=\frac{d}{2}=\frac{26}{2}=13\) ft.
The formula for the area of a semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\).
Substitute \(\pi = 3.14\) and \(r = 13\) into the formula: \(A_{semicircle}=\frac{1}{2}\times3.14\times13^{2}=\frac{1}{2}\times3.14\times169 = 265.33\) \(ft^{2}\).

Step3: Calculate the total area of the garden

The total area \(A = A_{rectangle}+A_{semicircle}\).
\(A=858 + 265.33=1123.33\) \(ft^{2}\).

Answer:

\(1123.33\) \(ft^{2}\)