4. A rectangle of 19 cm $\times$ 65 cm is divided by lines parallel to its sides into squares with a side of 1 cm. Into how many parts will this rectangle be divided if we also draw its diagonal?
65.4. The diagonal intersects $19+65-1$ cells, and, consequently, 83 parts are added to the initial partition. The total number of parts is $19 \cdot 65+83=1318$.