A fenced yard that is 200 feet wide and 300 feet long needs to be treated along a 6-inch band on the inside and a 6-inch band on the outside of the fence. How many square feet will be treated?

To determine how many square feet need to be treated along the 6-inch bands on both the inside and outside of the fenced yard, we start by calculating the dimensions of the yard.

The yard is 200 feet wide and 300 feet long. First, we need to find the perimeter of the yard since we are treating bands along the fence. The perimeter (P) of a rectangle is calculated using the formula:

[ P = 2 \times (length + width) ]

Substituting the dimensions:

[ P = 2 \times (300 + 200) = 2 \times 500 = 1,000 \text{ feet} ]

Next, we calculate the area to be treated. Since there are bands of 6 inches on both the inside and outside, we convert the width of the band to feet. Six inches is equal to 0.5 feet. Thus, the total width that needs to be treated on both sides of the fence is:

[ 0.5 + 0.5 = 1 \text{ foot} ]

Now, to find the total area to be treated, multiply the perimeter by the total width of the band:

[ \text{Area} = P