This one may look more complicated than Pandora's,
but it turns out "beautifully simple"!

Area of triangle ABC is 13824 square feet.
The length of line segment BD is 4/15 of line segment AB.
The length of line segment CE is 5/12 of line segment AC.
The length of line segment AF is 3/20 of line segment AB.
What is the area of triangle DEF?

Area of triangle EBC = (5/12) Area of triangle ABC = (5/12)13824 = 5760
Area of triangle ABE = 13824-5760 = 8064

Length of segment DF = Length of sement AB - (4/15 + 3/20)Length of segment AB
= (7/12)Length of segment AB

Area of triangle DEF = (7/12)Area of triangle ABE = (7/12)8064 = 4704

Good one!

Yepper CC!

k = Area of triangle ABC (13824)
u = BD/AB (4/15)
v = CE/AC (5/12)
w = AF/AB (3/20)
General case formula:
Area of triangle DEF = k * (1 - u - w) * (1 - v)

13824 * (1 - 4/15 - 3/20) * (1 - 5/12) = 4704

Surprisingly simple formula...