Final answer:
To determine the area of squares on a grid, count the grid squares within each figure or calculate side² if the side length is given. For figures with a known scale factor, adjust the dimensions accordingly before calculating the area. To compare areas, divide the area of the larger square by that of the smaller square to find the ratio.
Step-by-step explanation:
To find the area of each square, we must calculate the space inside the square's boundaries. As each grid square represents 1 square unit in the given problem, we first count the number of grid squares within each square figure to determine their areas. If we have both a smaller square and a larger square, we can find the area of the larger square by multiplying the dimensions of the smaller square by the scale factor provided, if any.
For example, if the side length of the smaller square is 4 units and that of the larger square is twice as much (scale factor of 2), then the side length of the larger square would be 4 units x 2, which is 8 units. The area of the smaller square is side² which equals 4 units x 4 units = 16 square units. For the larger square, the area is side² which equals 8 units x 8 units = 64 square units.
When comparing the two areas, we take the ratio of the larger to the smaller. In this case, 64 square units (larger square area) divided by 16 square units (smaller square area) gives us a ratio of 4:1, which means the area of the larger square is 4 times larger than the area of the smaller square. This exemplifies the rule that the ratio of areas of similar figures is the square of the scale factor.