2. A large square is divided into smaller squares. In one of the smaller squares a diagonal is also drawn, as shown. What fraction of the large square is shaded?
A $\frac{4}{5}$
B $\frac{3}{8}$
C $\frac{4}{9}$
D $\frac{1}{3}$
E $\frac{1}{2}$
SOLUTION
The shaded square in the lower right corner of the large square is $\frac{1}{4}$ of the large square. The shaded triangle is half of $\frac{1}{4}$ of the large square. Hence it is $\frac{1}{8}$ of the large square. The two small shaded squares in the upper left corner together are half of $\frac{1}{4}$, or $\frac{1}{8}$, of the large square. Therefore the fraction of the large square that is shaded is $\frac{1}{4}+\frac{1}{8}+\frac{1}{8}=\frac{1}{2}$.