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It depends on the pyramid.

If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section.

Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.

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Q: How Do you make a cross section of a parallelogram from a pyramid?
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