Notes
four squares and a triangle solution

Solution to the Four Squares and a Triangle Puzzle

Solution by Similar Triangles and Area of a Square and Triangle

With the points labelled as above, since $E C A$ is a straight line, triangles $E D C$ and $C B A$ are similar. This means that the lengths of $E D$ and $D C$ are in the ratio $3 : 1$. Since the lengths of $A B$ and $C D$ add up to the length of $E D$, this means that the lengths of $E D$ to $A B$ are in the ratio $3 : 2$.

Taking one unit as the length of $C D$, so then $A B$ has length $2$ and $E D$ has length $3$, the area of triangle $A E G$ is $\frac{1}{2} \times 2 \times 3 = 3$. The area of all four squares is $3 \times 4 + 9 = 21$.

Therefore the yellow triangle covers $\frac{3}{21} = \frac{1}{7}$th of the total area.