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. 38. 47 units2 94. 99 units2 153. 86 units2 379. 94 units2.

Answer 1

The area of the circle whose circumference is equal to the perimeter of the square is 38.47 squared units.

What is circumference and area of the circle?

Circumference of the circle is the length of its boundary. It can given as,

$P=2\pi r$

The area of the circle is the space occupied by it. It can be given as,

$A=\pi r^2$

Here (r) is the radius of the circle.

A square has a side that measures 5. 5 units. The perimeter of the square is the equal to the 4 times of its side. Thus its perimeter is,

$P=4\times5.5\\P=22\rm\; units$

The circumference of the circle is equal to the perimeter of the square. Thus the radius (r) of circle is,

$P=2\pi r\\22=2\times\pi r\\r\approx3.5\rm\; units$

The area of this circle is,

$A=\pi r^2\\A=3.14\times (3.5)^2\\A=38.465\\A\approx 38.47\rm\; units^2$

Hence the area of the circle whose circumference is equal to the perimeter of the square is 38.47 squared units.

Learn more about the circumference and area of the circle here;

brainly.com/question/402655