Answer:
The area of a circle with a circumference that equals the perimeter of the square is 9.62 units²
Step-by-step explanation:
The first thing we must do is find the perimeter of the square. In the problem, we are given that one of the side measurements of the square is 2.75 units. In order to find the perimeter of this square, we must multiply 2.75 by 4 because a square has four equal side measurements.
2.75 × 4 = 11
So, the perimeter of the square is 11 units. This number will also be the number for the circumference of the circle as mentioned in the problem. So, the circumference of the circle is 11 units. Now, we must find the radius of the circle so we can find the area. Let's use the formula for finding radius given the circumference.
[tex]Radius = \frac{circumference}{2\pi}[/tex]
Now, let;s plug in 11 for the circumference because our circumference is 11 units.
[tex]Radius=\frac{11}{2\pi}[/tex]
Multiply 2 by pi. We will use 3.14 in replacement of pi.
[tex]Radius=\frac{11}{6.28}[/tex]
Now, divide.
[tex]Radius=1.75[/tex]
So, our radius is 1.75 units. We can know use this number to find the area of the circle.
[tex]Area=r^2\pi[/tex]
Plug in 1.75 for the radius.
[tex]Area=(1.75)^2\pi[/tex]
Simplify the exponent.
[tex]Area=(3.0625)\pi[/tex]
Multiply the numbers.
[tex]Area=9.61625[/tex]
Lastly, we round this number to the nearest hundredth as it is asked of us in the problem.
9.61625 = 9.62
So, the area of the circle is 9.62 units²
