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It means the base in a 3D figure. For example, if it was a pyramid. the bottom part would be the base and you get the area of that base
A triangular base pyramid would fit the description.
Sometimes. Any face can be defined as a base of a prism; but pyramids may have one face that is a base and not a triangle.
Sometimes because a sphere which is a 3d figure has a diameter
It isn't clear how you would define the "perimeter" for a 3D figure. The base is the product of length x width.