两个大小不同的正方形如图所示。在两个正方形重叠的地方形成了一个未涂色的正方形。阴影部分 A 的面积与阴影部分 B 的面积之差为 24 $\text{cm}^2$。求未涂色部分的面积。 答：___ $\text{cm}^2$

1. Express the difference in area between the two squares.

Let the side of the large square be $L$ and the small square be $S$.
Area of A = $L^2 - \text{Area of unshaded part}$
Area of B = $S^2 - \text{Area of unshaded part}$
Difference = Area of A - Area of B = $L^2 - S^2 = 24$

2. Relate the side lengths to the total width.

Let the side of the unshaded square be $x$.
Total width = $L + S - x = 10 \implies x = L + S - 10$
Since $x > 0$, we must have $L + S > 10$. Also, $x$ must be smaller than $S$.

3. Find integer values for L and S that satisfy the conditions.

We need two square numbers whose difference is 24.
Possible squares: 1, 4, 9, 16, 25, 36, 49, 64...
Notice that $49 - 25 = 24$.
So $L^2 = 49 \implies L = 7$ cm
$S^2 = 25 \implies S = 5$ cm
Check condition: $L + S = 7 + 5 = 12 > 10$.

4. Calculate the area of the unshaded part.

Side of unshaded square $x = L + S - 10 = 12 - 10 = 2$ cm.
Area of unshaded part = $2 \times 2 = 4 \text{ cm}^2$.