4. A rectangle $10 \times 20$ is divided into unit squares. How many triangles are formed after drawing one diagonal?

![](https://cdn.mathpix.com/cropped/2024_05_06_0908da87f41f86dad345g-1.jpg?height=239&width=425&top_left_y=1387&top_left_x=1514)
Answer: 220.

Solution. The figure shows one of the obtainable triangles. All such triangles are right-angled, and the vertex of the right angle can be any lattice node, 
except those lying on the diagonal. There are a total of $21 \times 11$ nodes, and 11 of them are on the 

diagonal, so the number of triangles is $21 \times 11 - 11 = 220$.

Criteria. Any correct solution: 7 points.

Incorrectly accounting for nodes on the diagonal: 4 points.

Correct answer: 2 points.