Notes
four aligned squares solution

Four Aligned Squares

Solution by Area of a Triangle

With the points labelled as above, $C D$ is parallel to $I G$, so the area of triangle $I G D$ is the same as of $I G C$. The total area of rectangle $A C F H$ is $6 \times 5 = 30$. Triangle $G F C$ is half of square $G B C F$ so has area $10$. Triangle $I A C$ is half of rectangle $I A C E$ so has area $7.5$. Finally, triangle $H G I$ has area $2.5$. So the shaded triangle has area $30 - 10 - 7.5 - 2.5 = 10$.