Cutting and Covering - a cluster of questions

Two recent posts at mathoverflow are here and here.

We record some further questions:
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- Given an integer n, to cut n equal area isosceles triangles from the unit square that leave out as little of the square as possible.

- Given an integer n, to cover the unit square with equal area isosceles triangles such that the area of each covering unit is minimized.

Now, replace isosceles triangle with right triangles of equal area and we have two more classes of questions. Then replace unit square with whatever and there are many further questions.
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We have lots of work already done on cutting (or packing with) mutually congruent units from a specified shape or covering a specified shape with mutually congruent units. For example, Erich's Packing Center and in particular here . But cutting / covering with specified shapes with just equal area seems less studied.
Since merely covering a general triangle with a single least area isosceles triangle turned out to be a pretty tough question, most of the above questions might well be hard and there may not be any common pattern or algorithm.