It has just occurred to me that the digit check might only be there because you were using a buggy for loop. If so, the solutions are much simpler.

for:

my @fulls;
for my $area (@areas) {
    for my $short (@shorts) {
        push @fulls, "$short.area$area";
    }
}
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map:

my @fulls =
    map { my $area = $_; map "$_.area$area", @shorts }
    @areas;
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More intuitive map, but different order produced:

my @fulls =
    map { my $short = $_; map "$short.area$_", @areas }
    @shorts;
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NestedLoops:

use Algorithm::Loops qw( NestedLoops );

my @fulls = NestedLoops(
    [ \@areas, \@shorts ],
    sub { "$_[1].area$_[0]" },
);
[download]