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.

Answer 1

38.47 square units

Explanation:

All we have to do is first find the perimeter of the square (which is equal to the circumference of the circle), then find the radius of the circle and finally the area of the circle.

The square has a side that measures 5.5 units.

The perimeter of a square is given as:

P = 4L

where L = length of side of the square

Therefore, the perimeter of the square is:

P = 4 * 5.5 = 22 units.

This means that the circumference of the circle is 22 units.

The circumference of a circle is given as:

C = 2πR

and the area of a circle is given as:

`A = \pi R^2`

where R = radius

Therefore:

22 = 2πR

=> R = 22 / (2 * 3.14)

R = 22 / (6.28)

R = 3.50 units

The area is therefore:

`A = \pi * 3.50^2`

A = 38.47 square units

The area of the circle is 38.47 square units.