Puzzle 67: Square Cake Problem

A square cake is to be divided amongst 5 people so that each person has equal portions of cake and icing.  How should you cut the cake?  Hint: Need to have equal perimeter (icing) and area (cake) for each person.

NOTE: You cannot simply scrape off the icing!  You can only cut the cake.

Extension: How about cutting an equilateral triangle cake amongst 5 people?  And a regular hexagon cake amongst 5 people?
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