A2. Kristina drew 2 squares, the side lengths $\mathrm{v}$ in centimeters of which are natural numbers, and shaded the part of the larger square that lies outside the smaller square (see the figure). The area of the shaded region is $43 \mathrm{~cm}^{2}$. How many square centimeters is the sum of the areas of both of Kristina's squares?

![](https://cdn.mathpix.com/cropped/2024_06_07_e347356273e0c1397da7g-06.jpg?height=223&width=231&top_left_y=1168&top_left_x=1689)
(A) 882
(B) 925
(C) 968
(D) 1685
(E) 2022
A2. Let's denote the side length of the larger square in centimeters by $a$, and that of the smaller square by $b$. Then, $43=a^{2}-b^{2}=(a+b)(a-b)$. Since $a+b$ and $a-b$ are natural numbers and 43 is a prime number, it follows that $a+b=43$ and $a-b=1$. Therefore, $a=22$ and $b=21$. The sum of the areas of both of Kristina's squares is $a^{2}+b^{2}=484+441=925 \mathrm{~cm}^{2}$.