24. The diagram shows the square $W X Y Z$. The points $P, Q$ and $R$ are the midpoints of the sides $Z W, X Y$ and $Y Z$ respectively. What fraction of the square $W X Y Z$ is shaded?
A $\frac{3}{4}$
B $\frac{5}{8}$
C $\frac{1}{2}$
D $\frac{7}{16}$
$\mathrm{E} \frac{3}{8}$
24. E Label the intersection of $W Q$ and $X P$ as $V$ and the midpoint of $W X$ as $U$. Let the side-length of the square be 1 unit. The area of triangle $W X R$ is $\frac{1}{2} \times 1 \times 1$ units $^{2}=\frac{1}{2}$ units $^{2}$. Consider triangle $W X P$ and triangle $U X V$. These two triangles have the same angles and hence are similar. Since $U X$ is half of $W X$, it follows that $V U$ is half of $P W$ and hence has length $\frac{1}{4}$ unit. Therefore the area of triangle $W X V$ is $\left(\frac{1}{2} \times 1 \times \frac{1}{4}\right)$ units $^{2}=\frac{1}{8}$ units $^{2}$. Hence the shaded area is $\left(\frac{1}{2}-\frac{1}{8}\right)$ units $^{2}=\frac{3}{8}$ units $^{2}$. Therefore the fraction of the square that is shaded is $\frac{3}{8}$.