What is the area of a circle with a circumference that equals th perimeter of the square ?

  9.62 units²

Step-by-step explanation:

You can choose the appropriate answer with only a reasonable estimate. The circle with the same perimeter as the square will have a slightly larger area than the square. (about 27% larger) The area of the square can be estimated as slightly smaller than (3 units)² = 9 units². The one answer choice that is slightly larger than this is 9.62 units².

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If you want to actually figure it, you get ...

  C = P = 4s = 4·2.75 units = 11 units

The area of the circle in terms of the circumference is ...

  A = C²/(4π) = (11 units)²/(4π) = 121/12.56 units² ≈ 9.63376 units² ≈ 9.63 units²

The best match is to answer choice 9.62 units².

Using a higher precision value of π gives 9.6289 units², which still rounds to 9.63.