A dimension pertaining to the size of an object, generally within a horizontal axis.
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A game need not have a length or width. For example, "it" or "tag" is a game but if played in an open space (not a confined playground) there is no way to define its length or width.
The define the shape and size of a three dimensional object.
It isn't clear how you would define the "perimeter" for a 3D figure. The base is the product of length x width.
Length and width define two dimensions, like a piece of paper has a length distance measure along one side and a width distance measure on the other side. In three dimensions there is length and width and height, like a solid brick or block
You can define some things in terms of other things, but you will always need some starting point, something that is not formally defined. It makes sense to put "point" in this category. However, you can think of a point as an "object" that has zero length, zero width, and zero height.