Final answer:
The area of the book's picture, when scaled with a factor of 1 inch to 3 inches, is 972 square inches, which is determined by multiplying the original area by the square of the scale factor. Therefore, the correct answer is D.
Step-by-step explanation:
The student's question pertains to the concept of scale factor and its application to determining area measurements of similar figures. Given that the original book has an area of 108 square inches and the scale factor from the book to its picture is 1 inch to 3 inches, we must apply the scale factor to figure out the area of the book's picture. Since the area ratio is the square of the scale factor, and given that the scale factor of length is 1 to 3, the scale factor for area becomes 12 to 32, which is 1 to 9. Hence, we multiply the original area by the area scale factor to obtain the picture's area:
108 square inches × 9 = 972 square inches.
Therefore, the correct answer for the area of the book's picture is 972 square inches, which corresponds to option D.