How many unshaded squares are in the tenth figure of the pattern?
(A) 38
(B) 40
(C) 42
(D) 44
(E) 46
![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-117.jpg?height=262&width=760&top_left_y=2152&top_left_x=1119)
Solution 1

The first figure has 8 unshaded squares. The second figure has 12 unshaded squares. The third figure has 16 unshaded squares. So the number of unshaded squares increases by 4 with each new figure. So the number of unshaded squares in the tenth figure should be $8+4(9)=44$ (we add 4 nine times to get from the first figure to the second, from the second to the third, and so on).

## Solution 2

The first figure is a 3 by 3 square with a 1 by 1 square shaded in. The second figure is a 4 by 4 square with a 2 by 2 square shaded in. The third figure is a 5 by 5 square with a 3 by 3 square shaded in. Therefore, the tenth figure should be a 12 by 12 square with a 10 by 10 square shaded in. So the number of unshaded squares is $12^{2}-10^{2}=44$.

Answer: (D)