Question

a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 33 ft long and 22 ft wide. if the gardener wants to build a fence around the garden, how many feet of fence are required? (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 perimeter of the rectangle part

The rectangle has two sides of length \(33\) ft and one side of length \(22\) ft (the side with the semicircle is not included in the fence for that part). So the sum of these sides is \(33 + 33+22\).

$$33 + 33+22=88$$

Step2: Calculate the circumference of the semicircle

The formula for the circumference of a full - circle is \(C = \pi d\), for a semicircle \(C_{semicircle}=\frac{1}{2}\pi d\). Here, the diameter \(d = 22\) ft. Using \(\pi = 3.14\), we have \(C_{semicircle}=\frac{1}{2}\times3.14\times22\).

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Step3: Calculate the total length of the fence

Add the perimeter of the rectangle part and the length of the semicircle. \(L=88 + 34.54\)

$$L=122.54$$

Answer:

\(122.54\) ft