A certain dodgeball court is a circle with a square...

[AAPL]

A certain dodgeball court is a circle with a square perfectly inscribed inside it. The square represents the playing fiel, while the rest of the circle represents four rest areas for players. If the square has an area of 16, what is the area of the four rest areas combined?

$$\left(A\right)\ \ 4\pi\ -16$$
$$\left(B\right)\ \ 8\pi$$
$$\left(C\right)\ \ 8\pi-4\sqrt{2}$$
$$\left(D\right)\ \ 8\pi-16$$
$$\left(E\right)\ 16\pi-4\sqrt{2}$$

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Hi AAPL,

I'm going to give you some hints so that you can retry this question on your own:

[spoiler]
1) Since the square is inscribed in the circle, to answer this question we need to subtract the area of the square from the area of the circle.
2) The DIAGONAL of the square is EQUAL to the DIAMETER of the circle
3) You know the AREA of the square, so you can figure out the diagonal - it's based on a 45/45/90 right triangle
4) Divide the length of the DIAGONAL by 2 and you'll have the RADIUS of the circle...[/spoiler]

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

A certain dodgeball court is a circle with a square perfectly inscribed inside it. The square represents the playing fiel, while the rest of the circle represents four rest areas for players. If the square has an area of 16, what is the area of the four rest areas combined?

$$\left(A\right)\ \ 4\pi\ -16$$
$$\left(B\right)\ \ 8\pi$$
$$\left(C\right)\ \ 8\pi-4\sqrt{2}$$
$$\left(D\right)\ \ 8\pi-16$$
$$\left(E\right)\ 16\pi-4\sqrt{2}$$

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Since the area of the square is 16, each side is 4, and thus the diagonal of the square = the diameter of the circle = 4√2.

Since the radius is 2√2, the area of the circle is (2√2)^2 * π = 4 * 2 * π = 8π.

So, the area of the 4 rest areas combined is 8Ï€ - 16.

Answer: D