2 demensions is flat, 3 demensions is like the keyboard or the computer, not flat.
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The are no dimensions: the result is a pure number which is 24. "2 by 3 by 4" is a numerical expression: there are no dimensions associated with any of the three numbers and so there are no dimensions in their products.
A side (2-dimensions) or edge (3-dimensions).
area is 2, volume is 3
A rectangle has dimensions 7 ft x 12 ft. Which of the dimensions describe a rectangle that is similar to this rectangle?
That depends on the given dimensions which are not in the question.