Final answer:
The area of a rhombus cannot be determined with only the perimeter and one diagonal length provided; we would need the length of both diagonals to calculate the area.
Step-by-step explanation:
To find the area of a rhombus with a perimeter of 40 and a short diagonal of 12, we first need to determine the length of each side of the rhombus. Since the perimeter is the total distance around the rhombus, we divide the perimeter by 4 (since a rhombus has four equal sides) to get the length of one side. So, one side is 40 ÷ 4 = 10 units.
Now, a rhombus can be thought of as two congruent triangles joined at their bases. The area of a rhombus is equivalent to the product of its diagonals divided by 2. However, we only have the length of the short diagonal, which is 12 units. This is not enough information to calculate the area since the length of the other diagonal is unknown. We cannot determine the area based on the given information, and therefore cannot select any of the answer choices provided.