A photo is 32cm by 20cm. It is to be mounted on cardboard in a photo frame with a 4cm border between the frame and the edge of the photo. What is the area of the cardboard that can be seen?

To find the area of the cardboard that can be seen, we first need to calculate the dimensions of the cardboard including the border, and then find the area of the visible part.

1. Dimensions of the photo: 32 cm by 20 cm.

2. Border width: 4 cm.

3. Total dimensions of the cardboard:

   • Width: $32 \, \text{cm} + 2 \times 4 \, \text{cm} = 32 \, \text{cm} + 8 \, \text{cm} = 40 \, \text{cm}$
   • Height: $20 \, \text{cm} + 2 \times 4 \, \text{cm} = 20 \, \text{cm} + 8 \, \text{cm} = 28 \, \text{cm}$

4. Area of the cardboard:

   $$\text{Area}_{\text{cardboard}} = \text{Width} \times \text{Height} = 40 \, \text{cm} \times 28 \, \text{cm} = 1120 \, \text{cm}^2$$

5. Area of the photo:

   $$\text{Area}_{\text{photo}} = 32 \, \text{cm} \times 20 \, \text{cm} = 640 \, \text{cm}^2$$

6. Area of the cardboard that can be seen:

   $$\text{Area}_{\text{visible}} = \text{Area}_{\text{cardboard}} - \text{Area}_{\text{photo}} = 1120 \, \text{cm}^2 - 640 \, \text{cm}^2 = 480 \, \text{cm}^2$$

Thus, the area of the cardboard that can be seen is 480 cm².