19. In the diagram, $P Q R S$ and $W X Y Z$ are congruent squares. The sides $P S$ and $W Z$ are parallel. The shaded area is equal to $1 \mathrm{~cm}^{2}$.
What is the area of square $P Q R S$ ?
A $1 \mathrm{~cm}^{2}$
B $2 \mathrm{~cm}^{2}$
C $\frac{1}{2} \mathrm{~cm}^{2}$
D $1 \frac{1}{2} \mathrm{~cm}^{2}$
E $\frac{3}{4} \mathrm{~cm}^{2}$
19. A Let the length of a side of $P Q R S$ and of $W X Y Z$ be $x \mathrm{~cm}$. Consider quadrilateral $Q X R W$.

The diagonals $Q R$ and $W X$ are perpendicular and of length $x \mathrm{~cm}$. Therefore the area of $Q X R W$ is half the area of a rectangle with sides equal in length to $Q R$ and $W X$ and hence is equal to $\frac{1}{2} \times Q R \times W X=\frac{1}{2} x^{2} \mathrm{~cm}^{2}$. Similarly, the area of quadrilateral $S W R Z$ is also $\frac{1}{2} x^{2} \mathrm{~cm}^{2}$. Therefore the total shaded area is $x^{2} \mathrm{~cm}^{2}$. However, the question tells us that the shaded area is equal to $1 \mathrm{~cm}^{2}$. Therefore $x^{2}=1$. Hence the area of $P Q R S$ is $1 \mathrm{~cm}^{2}$.