jmc

The side of the large square is $1+3+1=5$, so the area of the large square is $5^2=25$. The area of the middle square is $3^2$, and the sum of the areas of the two smaller squares is $2\ast 1^2=2$. Thus, the big square minus the three smaller squares is $25-9-2=14$. This is the area of the two congruent L-shaped regions. So the area of one L-shaped region is $\frac{14}{2}=7$, and the answer is $\boxed{7}$