Question

A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for π, and round your answer to the nearest hundredth. (1 point)

38.47 units2

94.99 units2

153.86 units2

379.94 units2

Answer 1

To find the area of a circle whose circumference equals the perimeter of a square, we'll first calculate the perimeter of the square, then the circumference of the circle, and finally the area of the circle.

1. **Calculate the perimeter of the square**:
- The formula for the perimeter \( P \) of a square is given by:
\[
P = 4 \times \text{side length}
\]
- Given the side length is 5.5 units:
\[
P = 4 \times 5.5 = 22 \text{ units}
\]

2. **Set the circumference of the circle equal to the perimeter of the square**:
- The formula for the circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
- Since we want the circumference to equal 22 units:
\[
2\pi r = 22
\]
- We can solve for \( r \):
\[
r = \frac{22}{2\pi} = \frac{22}{2 \times 3.14} = \frac{22}{6.28} \approx 3.5 \text{ units}
\]

3. **Calculate the area of the circle**:
- The formula for the area \( A \) of a circle is:
\[
A = \pi r^2
\]
- Substituting \( r = 3.5 \) units:
\[
A = 3.14 \times (3.5)^2 = 3.14 \times 12.25 \approx 38.47 \text{ units}^2
\]

Thus, the area of the circle is approximately **38.47 units²**.

The answer is:

**38.47 units²**