Okay, let's see if we can't figure out this one...
First, we are given the shape--rectangular--and then we are given the dimensions--10 inches by 11 inches.
Then we are told that it has a 1-inch border, and asked to find the area of that border.
So let's treat this as a subtraction problem:
Let F = the area of the picture frame = 10 inches * 11 inches = 110 square inches.
Now the border is 1 inch, and the border is on all four sides of the picture frame. So, the OUTSIDE of the border is the same size as the outside of the picture frame, and the INSIDE of the border is 1 inch less on all four sides:
Let C = the area INSIDE the border (or the area which the border surrounds)
= (10 inches - 1 inch - 1 inch) * (11 inches - 1 inch - 1 inch) = 8 inches * 9 inches = 72 square inches.
So now we can subtract the inside area from the area of the frame to get the area of the border:
Let B = the area of the border = F - C = 110 square inches - 72 square inches = 38 square inches
So the area of the border is 38 square inches.