What is the area of a rectangle with a length of 4   centimeters   cm

Choice B is correct. The area of a rectangle with length $\mathcal{l}$ and width $w$ can be found using the formula $A=\mathcal{l}w$. It’s given that the rectangle has a length of $4 \text{cm}$ and a width of $2 \text{cm}$. Therefore, the area of this rectangle is $\left(4 \text{cm}\right)(2 \text{cm})$, or $8 {\text{cm}}^2$.

Choice A is incorrect. This is the sum, $\text{in} \text{cm}$, of the length and width of the rectangle, not the area, $\text{in} {\text{cm}}^2$.

Choice C is incorrect. This is the perimeter, $\text{in} \text{cm}$, of the rectangle, not the area, $\text{in} {\text{cm}}^2$.

Choice D is incorrect. This is the sum of the length and width of the rectangle squared, not the area.