Notes
two neighbouring rectangles solution

Two Neighbouring Rectangles

Solution by Triangle Area

With points labelled as in the above diagram, the areas of the triangles can be calculated with $A G$ as their bases. Since they have the same areas, their “heights” above this base are the same, so the lengths of $A B$ and $D H$ are the same. This means that $D$ is the midpoint of $C H$ and so $G$ is the midpoint of $A D$. Therefore the area of the largest rectangle is four times the area of $A G B$, so is $40$. The smaller rectangle is then a half in lengths of the larger, so is a quarter in area. The total area of the rectangles is therefore $40 + 10 = 50$.