Problem 7: Topsy Turvy Triangles

I have two equilateral triangles, one pointing up and one pointing down.

The smaller triangle is placed on top of the larger triangles in such a way that the region where they overlap is hexagonal.

What is the perimeter of the overlapping region if:

1. The triangles have perimeter 8 and 10?
2. The triangles have perimeter x and y?
3. (Harder) What constraint must there be on the sizes of the triangles to ensure that it is possible for the shape of the overlapping region to be hexagonal?