Compute all parts of given question:
Question: A homogeneous right wedge of mass M, horizontal length L and height H rests on a horizontal plane, with the side L on the plane.
Part A: Find the position of the center of mass of the wedge by determining its vertical distance h from the horizontal plane and its horizontal distance d from the vertex of the right angle of the wedge.
Part B: A point mass m is stuck at the top corner of the wedge. Find the new position of the center of mass of the combined body by calculating the new h and d.
Express your knowledge to solve the above question. Thanks.