Hero's Formula

[sdrsa]

Freinds ,
I have given a project to find out area of a triangle with
the help of Hero's formula.In school we are using turbo c++3.0.
What I did is:

#include<iostream.h>
#include<conio.h>
#include<math.h>
void main()
{
clrscr();
float a,b,c,area,S;
cout<<"Enter a";
cin>>a;
cout<<"Enter b";
cin>>b;
cout<<"enter c";
cin>>c;   
S=((a+b+c)/2);
if(S<a || S<b||S<c)
  {
   cout<<"Invalid triangle!!!";
  }
else
  {
    area=sqrt(S*(S-a)*(S-b)*(S-c));
   cout<<"The area of triangle is "<<area;
  }
getch(); 
}
 
 

Just wondering If there is any other way also bcoz I doubt what I have used
in declaring a triangle as INVALID is correct or not.

[Banfa]

No it looks right to me.

For a valid triangle with sides a, b and c then

a + b > c
a + c > b
b + c > a

are all true i.e the sum of any 2 sides is greater than the 3rd side.

Put another way 3 lines a, b and can not make a valid triangle if any of

a + b <= c
a + c <= b
b + c <= a

are false

time those by 1/2

1/2(a + b) <= 1/2.c
1/2(a + c) <= 1/2.b
1/2(b + c) <= 1/2.a

and it still holds true, add 1/2.c to the first equation, 1/2 b to the second and 1/2 a to the third

1/2(a + b) + 1/2.c <= 1/2.c + 1/2.c
1/2(a + c) + 1/2.b <= 1/2.b + 1/2.b
1/2(b + c) + 1/2.a <= 1/2.a + 1/2.a

simplify

1/2(a + b + c) <= c
1/2(a + b + c) <= b
1/2(a + b + c) <= a

subsitute 1/2(a + b + c) = S gives and invalid triangle if

S <= c
S <= b
S <= a

which is close to what you have coded but not quite. You code passes as a valid triangle any three lines where a + b = c (or the other 2 combinations), this is not a triangle as it has no height, the 2 shorter lines would lay exactly on top of the longer line. Hero's forumla will calculate the area as 0.

As an example of this try lines 10, 5 and 5.

You can correct your code easily report this invalid case by changing < to <=

[sdrsa]

Thumbs up!!!
Great mind.SO fine.Thnks Mate.

[areyoudrugz]

i don't get it so kindly put the exact code pls cuz i really need this...
plsss thnx

[JosAH]

Google is your friend; it found this page for you.

kind regards,

Jos