Area of triangle with side lengths 8, 10, 12

• Jan 25th 2006, 08:52 PM
extreme_pi
Area of triangle with side lengths 8, 10, 12
How do you find the area of a triangle with side lengths of 8, 10, and 12? Reply within 24 hours after midnight tomorrow, I will go to bed so don't bother.

• Jan 25th 2006, 09:16 PM
CaptainBlack
Quote:

Originally Posted by extreme_pi
How do you find the area of a triangle with side lengths of 8, 10, and 12? Reply within 24 hours after midnight tomorrow, I will go to bed so don't bother.

One word "Heron's formula" - Oh that's two words.

Let $\displaystyle s$ be the semi-perimeter of a triangle with sides $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$, that is:

$\displaystyle s=\frac{a+b+c}{2}$.

Then area of the triangle is:

$\displaystyle \mbox{Area}=\sqrt{s(s-a)(s-b)(s-c)}$.

So in your case $\displaystyle s=\frac{8+10+12}{2}=15$ and so:

$\displaystyle \mbox{Area}=\sqrt{15(15-8)(15-10)(15-12)}\approx140.7$.

RonL

PS

You won't get banned for posting the same question multiple times, but the
duplicates will be deleted. This is so that people do not waste their time