https://r2.erweima.ai/mathbot/image/1721419484884naa07enw.jpg

The first drop down menu options are : 18.84,24.50,26.84,75.36

To determine the correct answers for the drop-down menus, let's break down the problem and calculate both the perimeter and the area of the figure.

### Given:
- The radius of the partial circle with center \(A\) is 4 feet.
- \(\pi \approx 3.14\).

### Step 1: Calculate the Perimeter
The figure consists of a quarter circle and the two line segments \(AC\) and \(AB\) which both equal the radius (4 feet each).

1. **Perimeter of the Quarter Circle**:
\[ \text{Circumference of a full circle} = 2\pi r = 2 \times 3.14 \times 4 = 25.12 \]
\[ \text{Circumference of a quarter circle} = \frac{1}{4} \times 25.12 = 6.28 \]

2. **Total Perimeter**:
\[ \text{Total Perimeter} = 6.28 + 4 + 4 = 14.28 \text{ feet} \]

### Step 2: Calculate the Area
The figure consists of a quarter circle.

1. **Area of the Full Circle**:
\[ \text{Area of a full circle} = \pi r^2 = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \]

2. **Area of the Quarter Circle**:
\[ \text{Area of the quarter circle} = \frac{1}{4} \times 50.24 = 12.56 \text{ square feet} \]

### Double Check:
- The quarter circle perimeter calculation seems correct.
- The total length sum matches the expected.

### Final Answers:
- The perimeter of the figure is **14.28** feet.
- The area of the figure is **12.56** square feet.

Do you want more details or have any questions?

Here are 5 related questions you might want to ask:
1. How do you calculate the circumference of a circle?
2. What is the formula for the area of a circle?
3. How do you determine the area of a quarter circle?
4. How do you add perimeters of combined shapes?
5. How do you round numbers to the nearest hundredth?

**Tip:** When dealing with circular shapes and their parts, always remember to adjust the full-circle formulas to match the fraction of the circle you are working with (e.g., half, quarter).

Learn how to calculate the perimeter and area of a quarter circle with a radius of 4 feet. This detailed guide covers the formulas for circle perimeter and area, including step-by-step calculations. Suitable for students in Grades 7-9.

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