Which of the following formulas corresponds to the area of a rectangle?

• A. A = πr^2
• B. A = l + w
• C. A = l x w
• D. A = 2(l + w)

Answer: (C)

The formula that corresponds to the area of a rectangle is derived from the dimensions of the rectangle, specifically its length and width. The area is calculated by multiplying the length (l) by the width (w). This relationship makes logical sense because you can think of the area as counting how many unit squares can fit inside the rectangle; each square has a side length of one unit, and the rectangle can fit a total of l squares along its length and w squares along its width, resulting in l times w squares in total.

In contrast, the other formulas refer to different measurements. For instance, one option involves πr², which is the formula for the area of a circle, indicating the proportion of a circle's area relative to its radius. Another option represents the sum of length and width, which yields the perimeter of the rectangle rather than its area. Lastly, the formula that includes 2(l + w) calculates the perimeter as well, with the factor of 2 indicating that both lengths and widths are being included twice, but it does not describe area. Therefore, the correct choice accurately computes the area of a rectangle.