In the diagram, $P Q R S$ is a rectangle. Also, $\triangle S T U, \triangle U V W$ and $\triangle W X R$ are congruent.

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-026.jpg?height=298&width=696&top_left_y=1824&top_left_x=671)

What fraction of the area of rectangle $P Q R S$ is shaded?
(A) $\frac{3}{7}$
(B) $\frac{3}{4}$
(C) $\frac{1}{2}$
(D) $\frac{3}{5}$
(E) $\frac{2}{3}$
Suppose that $S U=U W=W R=b$ and $P S=h$.

Since the width of rectangle $P Q R S$ is $3 b$ and its height is $h$, then its area is $3 b h$.

Since $S U=b$ and the distance between parallel lines $P Q$ and $S R$ is $h$, then the area of $\triangle S T U$ is $\frac{1}{2} b h$. Similarly, the area of each of $\triangle U V W$ and $\triangle W X R$ is $\frac{1}{2} b h$.

Therefore, the fraction of the rectangle that is shaded is $\frac{3 \times \frac{1}{2} b h}{3 b h}$ which equals $\frac{1}{2}$.

ANsWer: (C)