A certain dodgeball court is a circle with a square perfectly inscribed inside it. the square represents the playing field, 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?

Question

Daphne Hays

Mathematics

28 February, 02:36

A certain dodgeball court is a circle with a square perfectly inscribed inside it. the square represents the playing field, 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?

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Zackery Bentley · Answer 1

Exactly 8*pi - 16

Approximately 9.132741229 For this problem, we need to subtract the area of the square from the area of the circle. In order to get the area of the circle, we need to calculate its radius, which will be half of its diameter. And the diameter will be the length of the diagonal for the square. And since the area of the square is 16, that means that each side has a length of 4. And the Pythagorean theorem will allow us to easily calculate the diagonal. So: sqrt (4^2 + 4^2) = sqrt (16 + 16) = sqrt (32) = 4*sqrt (2) Therefore the radius of the circle is 2*sqrt (2). And the area of the circle is pi*r^2 = pi * (2*sqrt (2)) = pi*8 So the area of the rest areas is exactly 8*pi - 16, or approximately 9.132741229