21. A rectangle is placed obliquely on top of an identical rectangle, as shown.
The area $X$ of the overlapping region (shaded more darkly) is one eighth of the total shaded area.
What fraction of the area of one rectangle is $X$ ?
A $\frac{1}{3}$
B $\frac{2}{7}$
C $\frac{1}{4}$
D $\frac{2}{9}$
E $\frac{1}{5}$
21. D Let the area of each rectangle be $Y$. Then the total shaded area is $2(Y-X)+X=2 Y-X$. Therefore $X=\frac{1}{8}(2 Y-X)$. So $8 X=2 Y-X$, that is $9 X=2 Y$. Therefore $\frac{X}{Y}=\frac{2}{9}$.