The square $S T U V$ is formed of a square bounded by 4 equal rectangles. The perimeter of each rectangle is $40 \mathrm{~cm}$. What is the area, $\mathrm{in} \mathrm{cm}^{2}$, of the square STUV?
(a) 400
(c) 160
(e) 80
(b) 200
(d) 100

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-012.jpg?height=360&width=323&top_left_y=2247&top_left_x=1506)

#
The correct option is (a).

Let $C$ and $L$ denote the length and width, respectively, of each of the four rectangles. The perimeter of each rectangle is given by $2(C+L)$. Since this perimeter measures $40 \mathrm{~cm}$, we obtain $C+L=20 \mathrm{~cm}$. Notice, in the given figure, that the side of the square $S T U V$ is given by $C+L$. Thus, its area is $(C+L)^{2}=20^{2}=400 \mathrm{~cm}^{2}$.