The same area in a different shape
Start with a half yard of fabric, 18 inches long, then cut it in half across its width. For 44 inch wide fabric, the result is two 18 × 22 inch fat quarters before trimming.
A regular quarter-yard cut from that same bolt is 9 × 44 inches. Both have an area of 396 square inches, but the fat quarter gives you room for wider pieces.
Check the actual dimensions
Fat-quarter width depends on the original fabric width, and removing selvages reduces what you can use. Check the package or measure your piece rather than assuming every fat quarter is exactly 18 × 22 inches.
Pieces with equal areas do not necessarily fit the same cutting layout. For example, one 12 inch square fits within an untrimmed 18 × 22 inch rectangle but cannot fit within a 9 × 44 inch strip.