In the given figure, the side of the larger square measures $10 \mathrm{~cm}$ and the side of the smaller square measures $4 \mathrm{~cm}$. The diagonals of the larger square contain the diagonals of the smaller square. What is the area of the hatched region?

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-023.jpg?height=226&width=237&top_left_y=2074&top_left_x=1595)
Solution 1: The hatched region is a trapezoid with bases measuring 10 and $4 \mathrm{~cm}$. The height of the trapezoid, which is half the difference of the sides of the two squares, measures $\frac{1}{2}(10-4)=3$ $\mathrm{cm}$. Thus, the area sought is

$$
3 \times \frac{1}{2}(10+4)=3 \times 7=21 \mathrm{~cm}^{2}
$$

Solution 2: The area of the larger square minus the area of the smaller square is equal to 4 times the area sought. Thus, the area sought is

$$
\frac{10^{2}-4^{2}}{4}=\frac{100-16}{4}=25-4=21 \mathrm{~cm}^{2}
$$