Solver Hero's (or Heron's) Formula (Used to Find the Area of a Triangle Given its Three Sides)

Source code of 'Hero's (or Heron's) Formula (Used to Find the Area of a Triangle Given its Three Sides)'

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==section input
If you want to find the area of any triangle given three sides, then you can find the area using <a href=http://en.wikipedia.org/wiki/Heron%27s_formula>Hero's Formula</a> (also known as Heron's Formula). This is an alternative to the conventional area formula in which you need to know the base and the height of the triangle.

Enter the side lengths of the triangle (positive numbers only):

a = *[input a=3]

b = *[input b=4]

c = *[input c=5]

==section solution

perl

### hero's or heron's formula

### Subroutines

sub error
{
 my $message=$_[0];
 print " Error: $message ";
 return;
}

### End Subroutines

### Error Checking

if($a<0 or $b<0 or $c<0)
{
 error("Please input positive numbers only.");
 return;
}

if($a=~m/\D/ or $b=~m/\D/ or $c=~m/\D/)
{
   my @temp=($a,$b,$c);
   @temp=map{s/\.//, $_} @temp;
   foreach (@temp)
   {
      if($_=~m/\D/)
      {
         error("Please enter real numbers only (ie no fractions, variables, etc...).");
         return;
      }
   }
   
   
}

### End Error Checking
#print "

#*[Tex \\LARGE testing x=\\sqrt{2+\\frac{\\sin(x)}{x^2}}]

#";

print " In order to find the area of a triangle 'A' with side lengths of 'a', 'b', and 'c', we can use <a href=http://en.wikipedia.org/wiki/Heron%27s_formula>Hero's Formula</a>: ";

print " {{{A=sqrt(S(S-a)(S-b)(S-c))}}} where S is the semiperimeter and it is defined by {{{S=(a+b+c)/2}}} ";

print "Note: \"semi\" means half. So the semiperimeter is half the perimeter. ";

print " So let's first calculate the semiperimeter S: ";

print " {{{S=(a+b+c)/2}}} Start with the semiperimeter formula. ";

print " {{{S=($a+$b+$c)/2}}} Plug in {{{a=$a}}}, {{{b=$b}}}, and {{{c=$c}}}. ";

my $s=$a+$b+$c;
print " {{{S=($s)/2}}} Add. ";

$s=$s/2;
print " {{{S=$s}}} Divide. ";

print " ---------------------------------------- ";

print " {{{A=sqrt(S(S-a)(S-b)(S-c))}}} Now move onto <a href=http://en.wikipedia.org/wiki/Heron%27s_formula>Hero's Formula</a>. ";

print " {{{A=sqrt($s($s-$a)($s-$b)($s-$c))}}} Plug in {{{S=$s}}}, {{{a=$a}}}, {{{b=$b}}}, and {{{c=$c}}}. ";

my @differences=($s-$a,$s-$b,$s-$c);
print " {{{A=sqrt($s($differences[0])($differences[1])($differences[2]))}}} Subtract. ";

my $product=$s*$differences[0]*$differences[1]*$differences[2];
print " {{{A=sqrt($product)}}} Multiply. ";

my $ans="";
if($product>=0)
{
 $ans=sqrt($product);
 print " {{{A=$ans}}} Take the square root of {{{$product}}} to get {{{$ans}}}. "; 
}
else
{
 print " Since you CANNOT take the square root of a negative number, this means that no triangle can be formed given the sides of {{{a=$a}}}, {{{b=$b}}}, and {{{c=$c}}}. Try to draw the triangle with the given lengths (make sure to use a ruler) to confirm this. ";
 return;
}

print " So the area of the triangle with side lengths of {{{a=$a}}}, {{{b=$b}}}, and {{{c=$c}}} is";

print " roughly" if $ans=~m/\./;

print " {{{$ans}}} square units. ";

if($ans==0)
{
 print " Note: Since the area is zero, this means that a triangle isn't formed here. Instead, a straight line is formed. ";
}

==section output

==section check