# Thread: Area of triangle with side lengths 8, 10, 12

1. ## 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.

2. 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 $s$ 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

PS

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