The expression of $K-map$ is $c.\bar a$
so the expression should be in $POS$ form for $NOR$ gate
$\overline{\overline{c.\bar a}} = \overline{\bar c + a} $
Now the expression is in $POS$ form
NOTE : $\bar a , \bar a , \bar c \text { is given so no need to use NOT gate for that}$
So only 1 $NOR$ gate required