2024 AMC 10B Problem 10

Area ratios are unchanged by an affine map, so compute with $A = (0,0),$ $B = (1,0),$ $C = (1,1),$ $D = (0,1)$

Find $F$ as the intersection of line $AC$ with line $EB,$ then use the shoelace formula

Area ratios don’t change under an affine map, so drop in convenient coordinates: $A = (0,0),$ $B = (1,0),$ $C = (1,1),$ $D = (0,1),$ which makes $E = (0, \tfrac12).$ Line $AC$ is $y = x,$ and line $EB$ runs from $(0, \tfrac12)$ to $(1, 0);$ they cross at $F = (\tfrac13, \tfrac13).$ The shoelace formula gives quadrilateral $CDEF$ area $\tfrac{5}{12}$ and triangle $CFB$ area $\tfrac13.$ So the ratio is $\tfrac{5}{12} : \tfrac13 = 5 : 4.$ Therefore, the answer is A.