Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `9`, `5`, and `12`?

Answer 1

Heron's formula for finding area of the triangle is given by
`Area=sqrt(s(s-a)(s-b)(s-c))`

Where `s` is the semi perimeter and is defined as
`s=(a+b+c)/2`

and `a, b, c` are the lengths of the three sides of the triangle.

Here let `a=9, b=5` and `c=12`

`implies s=(9+5+12)/2=26/2=13`

`implies s=13`

`implies s-a=13-9=4, s-b=13-5=8 and s-c=13-12=1`
`implies s-a=4, s-b=8 and s-c=1`

`implies Area=sqrt(13*4*8*1)=sqrt416=20.396` square units

`implies Area=20.396` square units