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Choice B is correct. The area of a rectangle with length $l$ and width $w$ can be found using the formula $A=lw$. 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.