B2. A square with side 2 lies within a square with side 7. The sides of the smaller square are parallel to the sides of the larger square. What is the area of the black region?

![](https://cdn.mathpix.com/cropped/2024_04_17_cc4b7043530fb5206fd0g-1.jpg?height=294&width=303&top_left_y=1298&top_left_x=1522)
B2. 10

We split the black area from the problem into four triangles, two of which we have shaded gray. The two gray triangles both have a base of 2 and together have a height of $7-2=5$, which is the height of the large square minus the height of the small square. The combined area of the two gray triangles is thus $\frac{1}{2} \cdot 2 \cdot 5=5$. The same applies to the two black triangles. Therefore, the total area of the region is $5+5=10$.

![](https://cdn.mathpix.com/cropped/2024_04_17_913d083fb7ef425a6a93g-1.jpg?height=303&width=306&top_left_y=1185&top_left_x=1520)