Find the area of a rhombus whose diagonals have lengths of 63 cm and 64 cm.

A technician works with two square plates of side lengths 42 cm and 35 cm. From their combined area, a square portion with a side length of 28 cm is removed. What is the remaining area in cm2?

A square and a rectangle have the same perimeter. The length of the rectangle is twice its width. If the side of the square is 12 meters, what is the difference between the area of the square and the area of the rectangle?