To find the area of the shaded region, we need to subtract the area of the circle from the area of the square.
The side length of the square is given as 6, so the area of the square is 6^2 = 36.
The radius of the circle is half the length of the diagonal of the square. The diagonal length can be found using the Pythagorean theorem, where d^2 = 6^2 + 6^2, so the diagonal length d = √(36+36) = √72.
Therefore, the radius of the circle is r = d/2 = √72/2 = √18.
The area of the circle is given by πr^2, so the area of the circle is π(√18)^2 = 18π.
Finally, the area of the shaded region is the area of the square minus the area of the circle: 36 - 18π.
To find the area to the nearest tenth, we can use an approximation of π as 3.14 or 3.14159. Using 3.14, the area of the shaded region is 36 - 18(3.14) = 36 - 56.52 = -20.52. Since we cannot have a negative area, the nearest tenth will be 0.0.
Therefore, the area of the shaded region to the nearest tenth is 0.
The figure below shows circle O inscribed inside square ABCD. Find the area of the shaded region to the nearest tenth.
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