Two cevians. One crossing point. A red triangle and a yellow region fighting for territory. By the end of these 50 panels, you'll solve it cold — no matter how scary the ratio looks.
If two triangles share a height, their areas are in the same ratio as their bases. Share a base instead? Ratio follows the heights.
Area = ½ · base · height
Set D=(0,0), C=(1,0), B=(1,1), A=(0,1). Any point on a side becomes one letter — a fraction of the way along. Any triangle's area becomes one formula: the Shoelace Formula.
Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|
Draw A→F and D→E. Where they cross is point P. Once you know P's coordinates, every triangle and every leftover region in the rectangle is just a shoelace calculation away.