To find the area of a rectangle, you multiply its length by its width. In this case, Natalia's area rug measures 57 inches by 41 inches, so the area can be calculated as:
Area = Length × Width = 57 inches × 41 inches.
None of the provided expressions directly represent this multiplication. However, if we look for a relevant expression that might compute to the area, the right choice should involve the multiplication of those dimensions.
Among the given options, none accurately represent the multiplication needed to calculate the area. However, if we are looking for an expression that might yield the same result through calculation (though not directly stated), we must specifically look for terms that reflect the individual dimensions.
In summary, to calculate the area of Natalia's rug, the correct operation is \(57 \times 41\), but none of the provided choices is suitable. If forced to select an expression based on multiplication or addition of squares that imbue some meaning toward dimensions:
- 57² + 41² (which is an additive expression and avoids confusion in calculation but does not yield the area).
Going back to the provided choices, the accurate interpretation simply eludes our context for area directly. Therefore, the area of the rug cannot be exactly derived from the given options without simplification or incorrect assessments.
If you must choose one from the given options, one could argue for 57² + 41² as it is a summation of the squares of the dimensions. But to clarify, it should strictly be noted that this does not yield the area directly.
Lastly, the correct expression for the area calculation remains 57 × 41 for clarity's sake, though absent here.