Asquare is inscribed in a circle of diameter 12square root of 2 millimeters. what is the area of the shaded region?
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

Determine the area of the circle by the equation,
                                 A = πD²/4
Substituting,
                                 A = π(12 sqrt 2)² / 4 = 226.145 mm² = 72π mm²

Since the diameter of the circle becomes the diagonal of the square, the sides of the square measure 12 mm. The area is equal to 12 mm x 12 mm which is equal to 144 mm². The area of the shaded region is therefore,
                                            (72π - 144) mm²
The answer is the first choice. 

D.