We have:

CD.DA = 24; FD⋅DA2=9⇒FD⋅DA=18

=> FDCD=1824=34⇒FC=14CD

AB⋅BE2=4⇒AB⋅BE=8

⇒BEBC=824=13⇒EC=23BC

⇒SΔEFC=14CD⋅23BC2=16.242=42=2(cm2)

⇒SΔAEF=24−9−4−2=13(cm2)

We have:

CD.DA = 24; \(\dfrac{FD\cdot DA}{2}=9\Rightarrow FD\cdot DA=18\)

=> \(\dfrac{FD}{CD}=\dfrac{18}{24}=\dfrac{3}{4}\Rightarrow FC=\dfrac{1}{4}CD\)

\(\dfrac{AB\cdot BE}{2}=4\Rightarrow AB\cdot BE=8\)

\(\Rightarrow\dfrac{BE}{BC}=\dfrac{8}{24}=\dfrac{1}{3}\Rightarrow EC=\dfrac{2}{3}BC\)

\(\Rightarrow S_{\Delta EFC}=\dfrac{\dfrac{1}{4}CD\cdot\dfrac{2}{3}BC}{2}=\dfrac{\dfrac{1}{6}.24}{2}=\dfrac{4}{2}=2\left(cm^2\right)\)

\(\Rightarrow S_{\Delta AEF}=24-9-4-2=13\left(cm^2\right)\)

Hey! Correct explanation but you calculate incorrectly. Try again!