In the diagram, a $4 \times 9$ grid $P Q T V$ is formed from thirtysix $1 \times 1$ squares. Lines $P R$ and $U S$ are drawn with $R$ and $S$ on $Q T$. What is the ratio of the shaded area to the unshaded area?
(A) $5: 9$
(B) $9: 8$
(C) $4: 5$
(D) $9: 5$
(E) $5: 4$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-087.jpg?height=257&width=461&top_left_y=2186&top_left_x=1298)
The area of the entire grid is $4 \times 9=36$.

The area of $\triangle P Q R$ is $\frac{1}{2}(Q R)(P Q)=\frac{1}{2}(3)(4)=6$.

The area of $\triangle S T U$ is $\frac{1}{2}(S T)(U T)=\frac{1}{2}(4)(3)=6$.

The area of the rectangle with base $R S$ is $2 \times 4=8$.

Therefore, the total shaded area is $6+6+8=20$ and so the unshaded area is $36-20=16$.

The ratio of the shaded area to the unshaded area is $20: 16=5: 4$.

ANSWER: (E)