Each box on this grid represents one square inch. Roger cut out a quilt block pattern and placed it on the grid (Square A). From the pattern he made a larger sized quilt block (Square B). What is the ratio of the area of Quilt A to the area of Quilt B?

Since each box on the grid represents one square inch, we can count the boxes inside each quilt block to find the area.

Quilt A (Square A) has an area of 4 square inches.
Quilt B (Square B) has an area of 16 square inches.

Therefore, the ratio of the area of Quilt A to the area of Quilt B is 4:16 or simplified to 1:4.