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Choice D is correct. The area $A$, in square centimeters, of a rectangle can be found using the formula $A=lw$, where $l$ is the length, in centimeters, of the rectangle and $w$ is its width, in centimeters. It's given that the rectangle has a length of $36$ centimeters and a width of $34$ centimeters. Substituting $36$ for $l$ and $34$ for $w$ in the formula $A=lw$ yields $A=36\left(34\right)$, or $A=\mathrm{1,224}$. Therefore, the area, in square centimeters, of this rectangle is $\mathrm{1,224}$.

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

Choice B is incorrect. This is the perimeter, in centimeters, not the area, in square centimeters, of the rectangle.

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