8. $[x]$ represents the greatest integer not exceeding the real number $x$. The area of the figure formed by points satisfying $[x]^{2}+[y]^{2}=50$ on the plane is $\qquad$ .
8. 12 .

First, consider the case in the first quadrant.
When $x>0, y>0$, from $[x]^{2}+[y]^{2}=50$, we get
$$
\begin{array}{l}
\Rightarrow\left\{\begin{array} { l } 
{ 7 \leqslant x < 8 , } \\
{ 1 \leqslant y < 2 }
\end{array} \left\{\begin{array} { l } 
{ 5 \leqslant x < 6 , } \\
{ 5 \leqslant y < 6 ; }
\end{array} \left\{\begin{array}{l}
1 \leqslant x<2, \\
7 \leqslant y<8 .
\end{array}\right.\right.\right. \\
\end{array}
$$

Thus, the area of the figure formed in the first quadrant is 3.
Therefore, the area of the figure given in the problem is 12.