11. The square $F G H I$ has area 80 . Points $J, K, L, M$ are marked on the sides of the square so that $F K=G L=H M=I J$ and $F K=3 K G$. What is the area of the shaded region?
A 40
B 35
C 30
D 25
E 20
11. D Let $l$ be the length of $K G$. Then $F K=3 l$, and the sides of the square $F G H I$ are each $4 l$.
Since the area of the square is 80 , we have $(4 l)^{2}=80$, which is $16 l^{2}=80$; hence $l^{2}=5$.
By Pythagoras' Theorem, $J K^{2}=F J^{2}+F K^{2}=l^{2}+(3 l)^{2}=10 l^{2}$.
The shaded area is half the area of the square $J K L M$, i.e. half of $J K^{2}=\frac{1}{2} \times 10 l^{2}=5 l^{2}=5 \times 5=25$.