6. In the large square $A B C D$ on the right, the area is 1, and the other points are the midpoints of their respective sides.

What is the area of the shaded triangle?
6.【Solution】In the figure, there are three squares: large, medium, and small. Each square's area is $\frac{1}{2}$ of the previous one, so the area of the small square is $\frac{1}{4}$. Label the vertices of the small square with letters as shown in the right figure. It is easy to see that the area of triangle $\mathrm{JFG}$ = the area of triangle $\mathrm{IHG}$ = $\frac{1}{4} \times$ the area of square $\mathrm{EFGH}$, and the area of triangle $\mathrm{EJI}$ = $\frac{1}{4} \times$ the area of triangle $\mathrm{EFH}$ = $\frac{1}{8} \times$ the area of square $\mathrm{EFGH}$. Therefore, the area of the shaded triangle JGI = $\left(1-\frac{1}{4}-\frac{1}{4}-\frac{1}{8}\right) \times$ the area of the small square = $\frac{3}{8} \times$ the area of the small square = $\frac{3}{32}$.