For the given points A, B, and C find the area of the triangle with vertices A, B, and C. A(3,5,2), B(6,15,2), C(7,9,3) The area is (Type an exact answer, using radicals as needed.)Identify the surface defined by the following equation. x2 + y2 + 322 + 12x= -35 Select the correct choice below and fill in the answer boxes to complete your choice. O A. The surface defined by the equation is a hyperboloid of one sheet centered at( and is centered around the z-axis. In the xy-plane, the trace has length in the x-direction and length in the y-direction. B. The surface defined by the equation is a hyperboloid of two sheets centered at ( , , )and whose traces in the xy-plane are ellipses. The shortest distance between the two sheets is O C. The surface defined by the equation is an ellipsoid centered at that has length in the x-direction, in the y-direction, and in the z-direction. O D. The surface defined by the equation is an elliptic cone centered at and whose traces in the xy-plane are ellipses.Evaluate the following integral. 8 5-2y/3 12-2y - 3z dx dz dy O 8 5-2y/3 12 -2y - 3z dx dz dy = y 1 0 0 (Type an exact answer.)Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. (2x + arctan yz) dy- ( 4yz + ) ) dx, where C is the boundary of the square with vertices (0, 4), (1, 4), (1, 5), and (0, 5). $ (2x + arctan y? ) dy- (4)2 + x ) ax = (Type an exact answer.)