From the bottom-left corner of a square, lines go to the middle of the top side and to the middle of the right side; the diagonal from the top-left to the bottom-right corner is also drawn. How many triangles are there?

With the bottom-left corner as a vertex: the diagonal cuts all 4 lines leaving that corner, giving $\left(\genfrac{}{}{0ex}{}{4}{2}\right)=6$; the top side and the right side give 1 each, so 8. Away from that corner: one small triangle at the top, one at the right, and the half-square above the diagonal, 3. Total $8+3=11$.