Question

A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

Answer 1

`A=2sqrt182`

Explanation:

First, find the triangle's semiperimeter. The semiperimeter is one half the perimeter of the triangle, which can be represented for a triangle with sides `a,b,` and `c` as

`s=(a+b+c)/2`

Thus,

`s=(6+11+9)/2=13`

Now, use Heron's formula to determine the area of the triangle. Heron's formula uses only the side lengths of the triangle to find the triangle's area:

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

`A=sqrt(13(13-6)(13-11)(13-9))`

`A=sqrt(13xx7xx2xx4)`

`A=2sqrt182`