Question 93
Suppose a cube $ABCD$-$EFGH$ having a side length of $2012$ and a plane are placed in space, and the intersection of the plane and the cube forms a hexagon $IJKLMN$, where the points $I$, $J$, $K$, $L$, $M$, $N$ lie on the sides $AE$, $EF$, $FG$, $GC$, $CD$, $DA$, respectively, as shown in figure 3 below.
If $AI - GL = 8$, $CM - EJ = 6$, $FK - DN = 4$, determine the value obtained by subtracting the area of the hexagon $IJKLMN$ from the sum of the areas of the triangles $IKM$ and $JLN$. Here we denote for a line segment $XY$ its length also by $XY$.
If $AI - GL = 8$, $CM - EJ = 6$, $FK - DN = 4$, determine the value obtained by subtracting the area of the hexagon $IJKLMN$ from the sum of the areas of the triangles $IKM$ and $JLN$. Here we denote for a line segment $XY$ its length also by $XY$.