1. Volunteers are fencing a part of City Park for toddlers. The diagram shows the area of a park that will be fenced. How many feet of fencing will be used?

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UpStudy AI · Accepted Answer

We begin by noting that the diagram (not shown here) indicates that the fenced region is not a “regular” rectangle but rather a composite figure. In one common version of this problem the area to be fenced has the following features:

• A rectangle with a base and two vertical sides  
• A semicircular “cap” attached to one of the shorter sides of the rectangle

In the version we discuss here the diagram provides these measurements:

• The rectangle has a base of $$60$$ feet and a height of $$30$$ feet.  
• The semicircle is built on the top of the rectangle so that its diameter equals the vertical side of the rectangle, namely $$30$$ feet.

Because the fencing will go along three “straight‐line” sides (the entire bottom of the rectangle and both vertical sides) and then around the curved edge of the semicircle we proceed as follows.

**Step 1. Compute the total length of the straight sides.**

The three straight sides are  
 • the bottom of the rectangle: $$60$$ feet  
 • the left side: $$30$$ feet  
 • the right side: $$30$$ feet

Thus the straight portions add to  
$$
60 + 30 + 30 = 120\text{ feet.}
$$

**Step 2. Compute the length of the curved (semicircular) part.**

The semicircular arc is one–half the circumference of a full circle with diameter $$30$$ feet. A circle with diameter $$d$$ has circumference  
$$
C=\pi d.
$$
Thus, the full circumference would be  
$$
\pi (30)=30\pi\text{ feet,}
$$
and the arc length of the semicircle is half that:
$$
\frac{1}{2}(30\pi)=15\pi\text{ feet.}
$$

**Step 3. Find the total fencing needed by adding the two portions.**

Adding the straight sides and the curved arc we get
$$
120+15\pi\text{ feet.}
$$

This expression $$120+15\pi$$ (in feet) is the total amount of fencing used.

Thus, the answer is  
$$
\boxed{120+15\pi}.
$$
A total of $$120 + 15\pi$$ feet of fencing will be used.

Volunteers are fencing a part of City Park for toddlers.
The diagram shows the area of a park that will be
fenced. How many feet of fencing will be used?

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