Can you cut a cake fairly to solve this middle school math problem?

[brewer]

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5 cuts. Each running from the center to the outside edge. In the case of a 20 x 20 x 5 cake each cut needs to be 16 linear centimeters along the outside edge. That would give everyone 160 square centimeters of icing and 400 cubic centimeters of cake.

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Exactamundo.  But to elaborate

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Of course every one of the triangles have the same height regardless of where their base may be.  For those which straddle a corner, each can be dissected into two triangles with a common height whose bases sum to the same as the other.  So for a square with side length = 20, the base of each triangle must be 4(20)/5 = 16  and the combined sides of a piece which includes a corner, like your red one, where 12 + 4 = 16.  Since the height of both triangles remains 8, the combined area of the two triangles would be 12(8)/2 + 4(8)/2 which can be rewritten as (12 + 8)(8)/2.

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If that's what Losty has to do, none of you are getting equal portions of cake. Apologies Losty.