Final answer:
Without the visual context for the original question about the shaded square and congruent squares, it is impossible to provide a precise answer. However, for a similar question provided with sufficient information, the area of a square with sides twice the length of another is four times greater, illustrating the rule that the ratio of areas of similar figures is the square of the scale factor.
Step-by-step explanation:
The question asks to find the area of a shaded square in an image where there are two large congruent squares with sides of 7 units and four small congruent squares with sides of 3 units. Without the visuals, we need to rely on descriptions and geometry knowledge to provide an answer. To ascertain the area of the shaded square, we need to visualize or deduce how these squares are arranged relative to one another. However, given that no description of the arrangement is provided in the question, any precise calculation would be speculative. Therefore, I cannot provide an answer to this question since essential information is missing, such as the arrangement of the squares in relation to each other.
To address a similar problem presented, if we have a square with a side length of 4 inches, and another square with side lengths twice that of the first, we can determine the area of the larger square in relation to the smaller one. Since the larger square has a side length that is twice as long, 4 inches x 2 = 8 inches, and the area of a square is calculated by squaring the side length, the area of the larger square would be 64 square inches (8 inches x 8 inches), while the area of the smaller square is 16 square inches (4 inches x 4 inches).
Therefore, the area of the larger square is four times larger than that of the smaller square. This exemplifies the general rule that the ratio of the areas of similar figures is the square of the scale factor. If the scale factor is 2, as it is in this example, the area will be 2², or 4 times larger.