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rusak2 [61]
3 years ago
15

On a rectangular coordinate plane, a circle centered at (0, 0) is inscribed within a square with adjacent vertices at (0, -2√) a

nd (2√, 0). What is the area of the region, rounded to the nearest tenth, that is inside the square but outside the circle?

Mathematics
1 answer:
Pani-rosa [81]3 years ago
7 0

Answer:

  0.9 square units

Step-by-step explanation:

We assume you intend the vertices of the square to be (±√2, 0) and (0, ±√2). Then the diagonals of the square are 2√2 in length and its area is ...

  (1/2)(2√2)² = 4

The radius of the inscribed circle is 1, so its area is ...

  π·1² = π

and the area outside the circle, but inside the square is the difference of these areas:

  area of interest = 4 - π ≈ 0.858407

  area of interest ≈ 0.9

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