Final answer:
The surface area of similar figures can be calculated using the square of the scale factor based on their side lengths. For cubes, the surface area ratio is the square of the ratio of their corresponding sides.
Step-by-step explanation:
Understanding Surface Area of Similar Figures
When dealing with similar figures, the ratio of their surface areas is related to the square of the ratio of their corresponding linear dimensions. If you know the surface area of the larger figure, you can calculate the surface area of the smaller figure by finding the square of the scale factor. Given that the figures are cubes, the scale factor is the ratio of the sides.
Example Calculation
Let's consider your example with Marta's squares. If the larger square has side lengths that are twice as long as the smaller square, the area of the larger square is four times the area of the smaller square because the area is proportionate to the square of the side lengths (area ratio = larger side length / smaller side length)² which is (2/1)² = 4.
The same principle can be applied to find the surface area of similar three-dimensional figures. In the case of similar cubes, if we know the volume ratio and the surface area of the larger cube, we can compare the two areas by using the cube of the scale factor for volume and the square of the scale factor for surface area.