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Choice C is correct. The area $A$, $\text{in} \text{square} \text{centimeters} \left({\text{cm}}^2\right)$, of a square with side length $s$, $\text{in} \text{cm}$, is given by the formula $A=s^2$. It’s given that the square has a side length of $55 \text{cm}$. Substituting $55$ for $s$ in the formula $A=s^2$ yields $A={55}^2$, or $A=\mathrm{3,025}$. Therefore, the area, $\text{in} {\text{cm}}^2$, of the square is $\mathrm{3,025}$.

Choice A is incorrect and may result from conceptual or calculation errors.

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

Choice D is incorrect and may result from conceptual or calculation errors.