No, but dimensions can be to negative powers. For example, the dimension for frequency is [T-1].
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A real physical rectangle on a piece of paper . . . no. Mathematically . . . if one of the dimensions is a negative length, then the area is negative.
They are not alike but they are related. A positive acceleration means an increase in velocity (speed). A negative acceleration means a decrease in velocity. Velocity (speed) has the dimensions of distance / time. Acceleration has the dimensions of distance/time2 or velocity/time.
On paper = 2 dimensions Physical = 3 dimensions Examples: a square is 2 dimensions and a cube is 3 dimensions a circle is 2 dimensions and a ball is 3 dimensions
A ray can be in 2 dimensions, in 3 dimensions, or in fact in any number of dimensions.
the plane, or xy plane, has two dimensions space has 3 dimensions