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Apart from a few cases it is not at all easy. You would need to consider all possible cross sections. In most cases the answer will depend on the relative measures of the different sides or edges.

A cube, for example, can have a cross section that is a point, line, triangle, square, rectangle, hexagon. The first two can be rejected since they have 0 area. But for the others, you would have to use differential calculus to determine the largest for that shape. It is, in fact, the rectangle from one edge of the cube to the diagonally opposite edge. The area is sqrt(2) times the side length.


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Q: How you determine the size of the largest possible cross section of ANY 3D solid?
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