Question

He side length of a smaller square is one-fourth the side length of a larger square. Which of the following statements describes the area of the smaller square?

A. The area of the smaller square is one-fourth the area of the larger square.
B. The area of the smaller square is equal to the area of the larger square.
C. The area of the smaller square is half the area of the larger square.
D. The area of the smaller square is three times the area of the larger square.

Answer 1

The area of the smaller square is one-sixteenth of the area of the larger square since the side length of the smaller square is one-fourth that of the larger square, meaning we square the fraction 1/4 to determine the area ratio.

Step-by-step explanation:

To determine which statement describes the area of the smaller square in comparison to the larger square, we need to understand the relationship between the side lengths and areas of squares. If the side length of the smaller square is one-fourth the side length of the larger square, the area of the smaller square would be one-fourth squared, because the area of a square is calculated by squaring its side length (area = side length × side length). Therefore, the area of the smaller square is one-sixteenth (1/16) of the area of the larger square, not one-fourth. Thus, the correct answer is none of the provided options.