Scheme 1: The diagonal of the rhombus is the length and width of the rectangle, and the area is 12 * 5/2 = 30 cm2.

Scheme 2: One diagonal of the diamond is the diagonal of the rectangle = 13 cm.

According to similar triangles, the length of the other diagonal is =13 * 5/12 = 65/12.

The rhombic area =13 * 65/12/2 = 845/24.

Therefore, the larger area is the second scheme.

The longest perimeter is also the second scheme.