The dermatologist is having you prepare a dog for a skin allergy test. Forty antigens need to be tested and each antigen must be 1 cm from the next. What size patch should you shave on the dog (assume that you are shaving a square)

To determine the size of the patch that needs to be shaved on the dog for the skin allergy test, you first need to calculate the total area required for all the antigens.

Since each antigen must be 1 cm away from the next, this means that there should be a 1 cm gap between each antigen. So, the length and width of each antigen's patch, including the gap, would be 2 cm.

The total area required can be calculated by multiplying the length and width of each antigen's patch by the number of antigens. In this case, there are forty antigens to be tested.

Total area required = (Length + Gap) * (Width + Gap) * Number of antigens

Total area required = (2 cm + 1 cm) * (2 cm + 1 cm) * 40 antigens

Total area required = 3 cm * 3 cm * 40 antigens

Total area required = 9 cm^2 * 40 antigens

Total area required = 360 cm^2

Therefore, you should shave a square patch on the dog that is approximately 360 cm^2 in size in order to test all forty antigens with a 1 cm gap between each.