This is a pattern block train. It starts with one triangle and adds one triangle at a time. I need the formula for these but the actual size is unknown. It becomes a four sided figure when the second triangle is added to it. I need the formulas for 1, 2, 3, 4, 5, 12,20,and 100.

What is the formula for these perimeters

Can you give any more details?

If two similar triangles are to be joined and they form a four sided figure, it means they must be joining at their longest side, in the case they are right-angled isosceles, forming a square.