Final answer:
Julia's tile design has an area of 64 square inches, calculated by multiplying the 8 by 8 grid of 1 square inch tiles.
The area of a square with side length twice that of another square is four times greater.
Step-by-step explanation:
The question involves finding the area of Julia's tile design which was created using square tiles laid out in an 8 by 8 grid.
Since each tile has an area of 1 square inch, we can calculate the total area of the design by multiplying the number of tiles in one row by the number of tiles in one column.
This calculation is simply 8 tiles × 8 tiles, which equals 64 square inches. Therefore, the area of Julia's tile design is 64 square inches.
In relation to the reference information provided, to compare the areas of two squares when the side length of the second square is twice the length of the first, we must first recognize that the area of a square is found by squaring the side length.
If the first square has a side length of 4 inches, the area is 4 inches × 4 inches = 16 square inches.
Doubling the side length to 8 inches for the larger square yields an area of 8 inches × 8 inches = 64 square inches.
Comparing the two areas (64 square inches to 16 square inches), we find that the larger square's area is four times greater than that of the smaller square.