2. Michelle had a valuable stamp mounted and framed. The stamp is $3 \mathrm{~cm}$ by 2.5 $\mathrm{cm}$ and the frame is a $9-\mathrm{cm}$ square. What is the area of the background not covered by the stamp?

Step 1 ：Given that the stamp is a rectangle with dimensions $3 \mathrm{~cm}$ by $2.5 \mathrm{~cm}$, and the frame is a square with side length $9 \mathrm{~cm}$.

Step 2 ：The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the stamp is $3 \mathrm{~cm} \times 2.5 \mathrm{~cm} = 7.5 \mathrm{~cm}^2$.

Step 3 ：The area of a square is calculated by squaring its side length. Therefore, the area of the frame is $9 \mathrm{~cm} \times 9 \mathrm{~cm} = 81 \mathrm{~cm}^2$.

Step 4 ：The area of the background not covered by the stamp can be calculated by subtracting the area of the stamp from the area of the frame. Therefore, the area of the background is $81 \mathrm{~cm}^2 - 7.5 \mathrm{~cm}^2 = 73.5 \mathrm{~cm}^2$.

Step 5 ：Final Answer: The area of the background not covered by the stamp is \(\boxed{73.5} \) square cm.