  ### Author Topic: Help needed for geometry problem - The area of a triangle  (Read 12630 times)

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#### jack_in-a_box

• Guest ##### Help needed for geometry problem - The area of a triangle
« on: September 08, 2008, 23:15:04 PM »
Hello,

First, congratulations for the forum. You do not find easy forum that cover so many matters.

I think that my question is very easy for you, noobish in simple words, but i do not happen to be Einstein and i do not have so good relations with math

I need to know the area of a triangle. The bad thing is that this triangle, is not a special triangle like right triangle for example. And also, i do not happen to know not one height of any side. Isearch the internet and always find this B*H/2 formula, but i know the B(base) and not the H(height). I only know the sides of the triagle.

Is there a way to calculate the height from the 3 sides of the triangle and so to calculate the area?

Thank you for the help

#### serafino

• Guest ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #1 on: September 08, 2008, 23:38:33 PM »
Iam not sure but i think this is the answer.
If someone is sre lets confirm it

#### kam

• Hero Member
•     • • Posts: 1849 ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #2 on: September 09, 2008, 19:21:32 PM »
Iam not sure but i think this is the answer.
If someone is sre lets confirm it
No not exactly. He does not know C and X

Actually you can calculate for any given triangle 3 sides the area using the Herons formula. it goes like:

For and ABC triangle:
t=(A+B+C)/2 (so called semi-perimeter)

E = t x (t-A) x (t-B) x (t-C)

E = the area of the triabgle

So, if the area is ehat you search, then this is done with the Herons formula. If you need to calculate some height, as for example the attachment from serafino, you know the area and thus:

E = (C x H)/2 => H = 2E/C ...

#### serafino

• Guest ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #3 on: September 09, 2008, 19:58:22 PM »
Kam he saids that he knows the sides of the triagle so he knows also C side.

#### kam

• Hero Member
•     • • Posts: 1849 ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #4 on: September 10, 2008, 00:04:10 AM »
Kam he saids that he knows the sides of the triagle so he knows also C side.

But of course he does. How stupid of me. Now, let's see your way a bit...

We have:
B2 = H2 + (C-X)2 (1)
A2 = H2 + X2 (2)

Obviously, we have 2 unknown values (X and H)  and 2 equations. This would lead to a solution. Let's see...

from (2) we have that H2 = A2 - X2 (3)

(1)due to (3) gives B2 =A2 - X2 + (C-X)2 =>

=> B2 = A2 - X2 +C2 + X2 -2CX =>
=> B2 = A2 - X2 + C2 + X2 -2CX =>
=> 2CX = A2 - B2 + C2 =>
=> X = (A2 - B2 + C2) / 2C

Tade Oper Deikse - In respect to the ancient Greek mathematician Pythagora

It was so stupid of me serafino. Answered very quickly.

#### jack_in-a_box

• Guest ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #5 on: September 16, 2008, 17:52:14 PM »
I think that the Herons formula is exactly what i was looking for...

Thanks for the solution!

#### kam

• Hero Member
•     • • Posts: 1849 ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #6 on: September 17, 2008, 14:01:42 PM »
Anytime. Keep visiting us.

#### alexinoos

• Guest ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #7 on: November 20, 2008, 18:09:00 PM »
Iam not sure but i think this is the answer.
If someone is sre lets confirm it
Actually you can calculate for any given triangle 3 sides the area using the Herons formula. it goes like:

For and ABC triangle:
t=(A+B+C)/2 (so called semi-perimeter)

E = t x (t-A) x (t-B) x (t-C)

E = the area of the triabgle

Let's apply your (not Herons) magic formula for A=5, B=4, C=3
t = 6, E = 6x1x2x3 = 36,
although the area of that triabgle is (4x3)/2=6 (...=Sqr(36))

#### kam

• Hero Member
•     • • Posts: 1849 ##### Re: Help needed for geometry problem - The area of a triangle
« Reply #8 on: November 20, 2008, 19:44:22 PM »
Iam not sure but i think this is the answer.
If someone is sre lets confirm it
Actually you can calculate for any given triangle 3 sides the area using the Herons formula. it goes like:

For and ABC triangle:
t=(A+B+C)/2 (so called semi-perimeter)

E = t x (t-A) x (t-B) x (t-C)

E = the area of the triabgle

Let's apply your (not Herons) magic formula for A=5, B=4, C=3
t = 6, E = 6x1x2x3 = 36,
although the area of that triabgle is (4x3)/2=6 (...=Sqr(36))