# A question on Heron's Formula...easy..but confusing..

• Dec 26th 2008, 08:57 PM
sudha_14
A question on Heron's Formula...easy..but confusing..
umm....can you guys please help me with this question??? i mean the formula is really easy..but i get confused in the middle...

Q. Find the area of a triangle whose sides are x, y and z, using Heron's Formula.

my doubt - here, s= x + y + z
2
so while substituting... the values are getting confusing..
• Dec 27th 2008, 12:17 AM
guigui51250
Hey

This formula is for the semiperimeter. To calcul the area, the Heron's formula is $\displaystyle A=\frac{\sqrt{(x^2+y^2+z^2)^2-2(x^4+y^4+z^4)}}{4}$

wiki definition
• Dec 27th 2008, 12:41 AM
sudha_14
i know Heron's formula...
it's
$\displaystyle \sqrt {s(s-a)(s-b)(s-c)}$

how come you got that?

and i WAS talking about the semi perimeter...
• Dec 27th 2008, 01:44 AM
mr fantastic
Quote:

Originally Posted by sudha_14
umm....can you guys please help me with this question??? i mean the formula is really easy..but i get confused in the middle...

Q. Find the area of a triangle whose sides are x, y and z, using Heron's Formula.

my doubt - here, s= x + y + z
2
so while substituting... the values are getting confusing..

You start by substituting for s:

$\displaystyle \sqrt{ \left( \frac{x+y+z}{2}\right) \cdot \left( \frac{x+y+z}{2} - x\right)} \cdot \left( \frac{x+y+z}{2} - y\right) \cdot \left( \frac{x+y+z}{2} - z\right)$.

Now you get common denominators and simplify the fractions in the second, third and fourth bracket. Then simplify.

It would help if you showed where you're stuck.