How many triangles

We note that a triangle is formed by any two slanting/vertical lines and one horizontal line. The number of ways to choose two slanting/vertical lines from six is $\dbinom 62$ and that to choose a horizontal line from five is $\dbinom 51$ . Therefore, the total number of triangles is $\dbinom 62 \dbinom 51 = 15 \times 5 = \boxed{75}$ .

The answer is 75 because there is 5 rows and 5 columns

5(6)=30/2=15(5)=75