A pentagon has its top corner joined to both bottom corners, and its two side corners are joined by a flat line. Find the number of triangles.

From the top corner four lines go down (two sides and two inner lines); the flat line cuts all four, giving $\left(\genfrac{}{}{0ex}{}{4}{2}\right)=6$. The base closes the big middle triangle, 1. On each side, the top corner, a side corner and a bottom corner make 1, and the side corner, the flat line and an inner line make 1: 4. Total $6+1+4=11$.