1) To find the area of a circle bounded by a circle circumscribed about a square, we can use the formula:
S = πr ^ 2, in our case r is equal to half the hypotenuse of a right triangle.
2) By the Pythagorean theorem, we find the hypotenuse of a right triangle:
c = √ (a ^ 2 + b ^ 2) = √ ((8√2) ^ 2 + (8√2) ^ 2) = √ (2 * 64 * 2) = √256 = 16.
3) Since r = c / 2 = 16/2 = 8, then:
S = πr ^ 2 = π * 8 ^ 2 = 64π = 64 * 3.14 = 200.96 (square units).
Answer: the area of a circle bounded by a circle circumscribed about a square is 64π or 200.96 (square units).
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