## overlap tiling with isosceles triangle

Given a geometric shape of an arc (which can be taken as isosceles triangle )with area a

1. What will be the minimum number of triangles N needed to fill a given area A
2. What could be the maximum sub-area created by N' > N; a' <= a
3. Given N' give an algorithm to arrange triangles such that it minimize a',

First one shows area a. Second one shows subarea a'=a
Third and fourth are different ways with overlap which has three overlapped areas a1, a2 and a3. Assume that a1>a2>a3. I want to minimize a1.