jmc

We could count the area contributed by each square on the $3\times 3$ grid: Top-left: $0$ Top: Triangle with area $\frac{1}{2}$ Top-right: $0$ Left: Square with area $1$ Center: Square with area $1$ Right: Square with area $1$ Bottom-left: Square with area $1$ Bottom: Triangle with area $\frac{1}{2}$ Bottom-right: Square with area $1$ Adding all of these together, we get $6$ which is the same as $\boxed{6}$