Answer:
If the perimeter of a square picture frame is 12 inches, then each side of the square frame must be 3 inches long, since 4 x 3 = 12.
To find the area of the picture frame, we need to subtract the area of the picture from the area of the frame. Since the frame is a square with 3-inch sides, its area is 3 x 3 = 9 square inches.
However, we don't know the size of the picture, so we can't calculate its area directly. Instead, we can use the fact that the picture and the frame together form a larger square with sides that are 12 inches long (since the perimeter of the whole thing is 12 inches).
The area of this larger square is 12 x 12 = 144 square inches.
Since the area of the frame is 9 square inches, the area of the picture must be 144 - 9 = 135 square inches.
Therefore, the area of the picture frame is 9 square inches, and the area of the picture is 135 square inches.