The four vertices of a rectangle or square can be uniquely determined by two pairs of coordiates $(x_1, x_2)$ and $(y_1, y_2)$ where $x_1 \ne x_2$ denote the horizontal direction locations, and $y_1\ne y_2$ denote vertical direction locations. Hence, the problem can be expressed as selecting $2$ out of $11$ horizontal coordinates and $2$ out of $7$ vertical coordinates. This leads to the answer $${11\choose 2}{7\choose 2}=\boxed{1155}$$