What is the formula for the area of a rectangle?

The formula for the area of a rectangle is given by multiplying its length (l) by its width (w). This relationship is fundamental in geometry, as it reflects that the area is essentially the measure of how much space is contained within the rectangle. By using the formula A = lw, one can calculate the total number of square units that fit inside the rectangle.

When considering the other choices, the formula A = l^2 + w^2 does not apply to rectangles; it suggests a relationship between the sides that would be more relevant to specific types of problems, such as relating to squares or right triangles rather than area calculations. The formula A = l + w adds the dimensions together, which does not correlate with area measurement, as it yields a linear measurement rather than a two-dimensional space. Lastly, the formula A = 2l + 2w resembles the perimeter calculation of a rectangle, which encompasses the total distance around the shape but does not describe the area contained within it.

Therefore, the correct formula for determining the area of a rectangle is A = lw, reflecting the direct multiplication of the rectangle's length and width.