Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `8`, `4`, and `9`?

Answer 1

See below

Explanation:

Heron formula is `S=sqrt(s(s-a)(s-b)(s-c))` where

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

In our case `s=(8+4+9)/2=21/2`

Now `S=sqrt(21/2(21/2-8)(21/2-4)(21/2-9))=`

`=sqrt(21/2·5/2·13/2·3/2)=sqrt(4095/16)=(3sqrt455)/4` square units