Taking that hash idea a bit further, you could end up at a dispatch table, something like the following:

#!usr/bin/perl
use strict;
use warnings;

sub req_args {
    my $nArgs = @ARGV;
    die "$_[0] argument(s) required but $nArgs given!\n"
        if $_[0] != $nArgs;
}

my $pi=3.141592654;

my %dispatch = (
    tri => { area => sub { req_args(2); return 0.5*$ARGV[0]*$ARGV[1]; 
+     },
             peri => sub { req_args(3); return $ARGV[0]+$ARGV[1]+$ARGV
+[2]; },
             hypo => sub { req_args(2); return sqrt($ARGV[0]*$ARGV[0]+
+$ARGV[1]*$ARGV[1]); },
           },
    cir => { area => sub { req_args(1); return $ARGV[0]*$ARGV[0]*$pi; 
+     }, #radius
             peri => sub { req_args(1); return $pi*$ARGV[0];          
+     }, #diameter
             hypo => sub { die "Option 'hypo' only allowed for triangl
+e."  },
           },
    rec => { area => sub { req_args(2); return $ARGV[0]*$ARGV[1];     
+     },
             peri => sub { req_args(2); return 2*($ARGV[0]+$ARGV[1]); 
+     },
             hypo => sub { die "Option 'hypo' only allowed for triangl
+e."  },
           },
    sqr => { area => sub { req_args(1); return $ARGV[0]*$ARGV[0];     
+     },
             peri => sub { req_args(1); return 4*$ARGV[0];            
+     },
             hypo => sub { die "Option 'hypo' only allowed for triangl
+e."  },
           },
);

die "You need to specify at least 3 args." if @ARGV < 3;

# $what to calculate on $which type of figure
my ($which, $what) = (shift, shift);

die "Unknown type '$which' of figure."     unless exists $dispatch{$wh
+ich};
die "Unknown type '$what' of calculation." unless exists $dispatch{$wh
+ich}{$what};
print "The answer is ", $dispatch{$which}{$what}(), ".\n";
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