Notes
two perpendicular equilateral triangles solution

Solution to the Two Perpendicular Equilateral Triangles Puzzle

Note: for this to be a well-defined problem, the equilateral triangles are assumed to be the same size.

Solution by Similar Triangles and Lengths in an Equilateral Triangle

With the points labelled as above, triangles $A B C$ and $A D E$ are similar, and the scaling also takes one circle to the other. The scale factor is found by comparing the lengths of $A B$ and $A C$. That of $A B$ is half the side length of one of the equilateral triangles while that of $A C$ is $\frac{\sqrt{3}}{2}$ of the side length. So the ratio $A B : A C$ is $1 : \sqrt{3}$. The area scale factor is therefore $3$ and so the area of the larger circle is $3$.