Area of triangle with side lengths 8, 10, 12

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.

Anyways, help please!

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

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

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

Then area of the triangle is:

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

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

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

RonL

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