How do you use Heron's formula to find the area of a triangle with sides of lengths $18$ , $9$ , and $13$ ?

Question

1535 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-22T01:36:08

Heron's formula relates the area of a triangle to the side of the triangle

$A = sqrt((s)(s-a)(s-b)(s-c))$

Where s is the sum of the side lengths divided by 2.

So, first we find s, the semiperimeter

$18+9+13/2 = 20$

So $s=20$

Now we simply plug in the values into Heron's formula

$A = sqrt((20)(20-18)(20-9)(20-13))$

$A = sqrt((20)(2)(11)(7))$

$A = sqrt(3080)$

$A = 2sqrt(770)$

which is approximately 55.5

How do you use Heron's formula to find the area of a triangle with sides of lengths 18 18 , 9 9 , and 13 13 ?