In the diagram, $P Q R S$ is a square. Square $P Q R S$ is divided into five rectangles, as shown. The area of the shaded rectangle is
(A) 49
(B) 28
(C) 22
(D) 57
(E) 16

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-075.jpg?height=475&width=466&top_left_y=516&top_left_x=1296)

## Part B: Each correct answer is worth 6.
Solution 1

Since $P Q R S$ is a square and $Q R=2+9=11$, then $P Q=Q R=S R=P S=11$.

The height of the shaded rectangle equals the height of the top left rectangle minus the height of the top right rectangle, or $6-2=4$.

The width of the shaded rectangle equals the width of the top right rectangle minus the width of the bottom right rectangle.

Since $S R=11$, then the width of the bottom right rectangle is $11-10=1$.

Therefore, the width of the shaded rectangle is $8-1=7$.

Thus, the area of the shaded rectangle is $4 \times 7=28$.

## Solution 2

Since $P Q R S$ is a square and $Q R=2+9=11$, then $P Q=Q R=S R=P S=11$.

Since the side length of the square is 11 , then its area is $11^{2}=121$.

Since $P Q=11$, then the width of the top left rectangle is $11-8=3$, and so its area is $3 \times 6=18$.

Since $P S=11$, then the height of the bottom left rectangle is $11-6=5$, and so its area is $5 \times 10=50$.

Since $S R=11$, then the width of the bottom right rectangle is $11-10=1$, and so its area is $1 \times 9=9$.

The area of the top right rectangle is $8 \times 2=16$.

Thus, the area of the shaded rectangle equals the area of square $P Q R S$ minus the combined areas of the four unshaded rectangles, or $121-18-50-9-16=28$.

ANSWER: (B)