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A square is inscribed in a circle of diameter 12 millimeters. What is the area of the shaded region?
A square is inscribed in a circle with a diameter of 12 StartRoot 2 EndRoot millimeters. Everything outside of the square is shaded.
Recall that in a 45 – 45 – 90 triangle, if the legs each measure x units, then the hypotenuse measures x units.
(72π – 144) mm2
(72π – 72) mm2
(288π – 288) mm2
(288π – 144) mm2
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GPT-5 mini
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Diameter = 12√2 so radius = 6√2. Circle area = πr^2 = π(6√2)^2 = 72π.
An inscribed square has diagonal = diameter = 12√2. In a 45–45–90 triangle the diagonal = side·√2, so square side = (12√2)/√2 = 12 and square area = 12^2 = 144.
Shaded area = circle − square = 72π − 144 mm^2.
Answer: (72π − 144) mm^2.
An inscribed square has diagonal = diameter = 12√2. In a 45–45–90 triangle the diagonal = side·√2, so square side = (12√2)/√2 = 12 and square area = 12^2 = 144.
Shaded area = circle − square = 72π − 144 mm^2.
Answer: (72π − 144) mm^2.
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