Task 169

The task

Coplanar squares $ABGH$ and $BCDF$ are adjacent, with $CD = 10$ units and $AH = 5$ units. Point $E$ is on segments $AD$ and $GB$. What is the area of triangle $ABE$, in square units? Express your answer as a common fraction. [asy] draw((0,0)--(5,0)--(5,5)--(0,5)--(0,0)--cycle,linewidth(2)); draw((5,0)--(15,0)--(15,10)--(5,10)--(5,0)--cycle,linewidth(2)); draw((0,0)--(15,10),linewidth(2)); filldraw((0,0)--(5,0)--(5,10/3)--(0,0)--cycle,gray,linewidth(2)); label("A",(0,0),SW); label("B",(5,0),S); label("C",(15,0),SE); label("D",(15,10),NE); label("E",(5,10/3),SE); label("F",(5,10),NW); label("G",(5,5),NW); label("H",(0,5),NW); [/asy]